32 research outputs found
Gushel–Mukai varieties with many symmetries and an explicit irrational Gushel–Mukai threefold
No full textWe construct an explicit smooth Fano complex threefold with Picard number 1, index 1, and degree 10 (also known as a Gushel–Mukai threefold) and prove that it is not rational by showing that its intermediate Jacobian has a faithful PSL(2,F11)-action. Along the way, we construct Gushel–Mukai varieties of various dimensions with rather large (finite) automorphism groups. The starting point of all these constructions is an Eisenbud–Popescu–Walter sextic with a faithful PSL(2,F11)-action discovered by the second author in 2013
Devenir à long terme des patients admis en réanimation neurochirurgicale et victimes d' un hématome intracérébral d' origine primaire ou par malformation arterioveineuse
No full textEn dépit des progrès de leur prise en charge, le pronostic fonctionnel des patients victimes d'hématomes intracérébraux reste médiocre. Peu d'études tiennent compte des conséquences sociales à long terme. Nous comparons l'évolution de patients victimes d'hématomes d'origine primaire ou par rupture de malformation artérioveineuse, admis en réanimation neurochirurgicale, deux ans après l'accident, et recherchons des facteurs de risque de mauvaise évolution. Etude rétrospective monocentrique (Pitié-Salpêtrière) de Janvier 2005 à Décembre 2007. Recueil de l'ensemble des données cliniques, biologiques et radiologiques du séjour en réanimation neurochirurgicale. Entretien téléphonique deux ans après l'accident et évaluation du devenir fonctionnel. 40 patients admis pour hématome d'origine primaire, 23 pour hématome par rupture de malformation artérioveineuse, 19 patients perdus de vue. 18 % des patients sont décédés. 45 % ont un GOSE >= 5, sans différence entre les deux groupes étiologiques. 86 % des patients présentent au moins un trouble neuropsychologique. Les patients victimes de rupture de malformation artérioveineuse présentent plus de difficultés professionnelles (85 % versus 43 %). Seule l'instauration d'une ventilation mécanique au cours de la prise en charge apparaît comme un facteur de risque d'évolution défavorable. L'intensité des soins prodigués en réanimation neurochirurgicale améliore le pronostic des patients victimes d'hématome intracérébral primaire ou par rupture de malformation artérioveineuse. Un nombre important garde toutefois des séquelles neuropsychologiques. Une réflexion doit s'engager sur la qualité des scores pronostiques disponibles, et le bénéfice réel apporté aux patients.PARIS6-Bibl.Pitié-Salpêtrie (751132101) / SudocSudocFranceF
On the period domain of polarised K3 surfaces and hyper-Kähler manifolds of K3-type
No full textA hyper-Kähler manifold is a simply connected compact Kähler manifold whose space of holomorphic 2-forms is generated by an everywhere non-degenerate form. In dimension 2, hyper-Kähler manifolds are known as K3 surfaces. In the first part of the thesis we present the basic theory of hyper-Kähler manifolds, and in particular the construction of the period morphism for polarised K3 surfaces. The Torelli theorem proves that, for each polarization degree , the period morphism for polarized K3 surfaces of degree is an embedding of the moduli space for polarized K3 of degree into the period space , where is the lattice associated to a polarized K3 surface of degree 2d, and the period space is an arithmetic quotient of the period domain associated to . In the second part, we give a generalisation of Theorem 3.3 of the article “A finite group acting on the moduli space of K3 surfaces”, by Paolo Stellari, in which the author characterize the divisors contained in the fixed locus of some isometry of that acts nontrivially on the period space. We generalise his result to each finite Galois cover of an irreducible period space (quotient of the period domain associated to an even indefinite lattice of signature (2, ) by an arithmetic group). Moreover, we study the case of polarized hyper-Kähler manifolds of K-type
Spectroscopie de nanosondes hybrides à cœur métallique
No full textORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF
Complex tori and abelian varieties
No full textCollection : SMF/AMS Texts and Monographs, 11This book is a translation from the French of an expanded version of a graduate course given in 1997. The author states as its goal to offer an elementary introduction to the classical theory of complex tori while presenting in parallel a more "modern" point of view using more recent theories (sheaves, Chern classes, cohomology, etc.). Now this goal is attained: The text is skillfully streamlined so that, to cover a large amount of important and different topics, it needs only a one-page bibliography. To keep the discussion smooth, some more complicated definitions and proofs are (mainly in the last chapters) referred to the literature and/or explained in footnotes, which also contain more references than the bibliography at the end of the book. Every chapter has at its end several interesting exercises. The author treats in the first two chapters the classical theory of one-dimensional complex tori, elliptic curves and their moduli, and then states as his purpose to generalize these results to arbitrary dimension. Thus, in the next chapters the classical theory of complex tori is presented, intertwined with the now usual tools from analytic and algebraic geometry, i.e., differential forms and de Rham cohomology (in Chapter 3), theta functions and divisors (Chapter 4), line bundles, sheaf cohomology, and first Chern class (Chapter 5). Among others, we find as main results Weil's theorem that any effective divisor on a complex torus is the divisor of a theta function (Theorem 4.9), and the Appell-Humbert theorem parametrizing the line bundles on a complex torus by their types (Theorem 5.17). In Chapter 6 abelian varieties are introduced (in relation to Riemann conditions) and their projective imbedding is presented together with (among others) the standard facts about their field of meromorphic functions and their endomorphisms. Chapter 7 treats moduli spaces of polarized abelian varieties using Riemann's theta functions. We see projective embeddings of the moduli spaces via theta constants. Finally, Chapter 8 assembles several newer non-standard results concerning subvarieties of a complex torus. We find connectedness results and discussions of fundamental groups. Here the text is no longer as elementary as in the beginning and relies on more recent papers cited in footnotes. As examples, we indicate the Conjecture in 8.3: Let be a complex torus, and let be an irreducible nondegenerate subvariety of which is a local complete intersection. We have Another example is the final Corollary 15 saying that the canonical bundle of a smooth subvariety of a complex torus that is invariant under translation by any nontrivial torus is ample
Spectroscopie de nanosondes hybrides à coeur métallique
No full textFluctuation Correlation Spectroscopy has been used to characterize the optical response of molecules and individual gold nanobeads, in solution. The latter are functionalized or not, and are aimed to be used as new biochemical nanoprobes. All the experiments were carried on an optimized confocal or/and biphotonic microscope in order to detect very weak signals. Several filtering procedures of the fluorescence signal and correlation calculation algorithms were used to precisely analyze the data. I show that the impulsional tensorial response of the microscope has to be taken into account to fit the correlation curves of particles with an anisotropic emission diagram. I have studied three different kinds of nanoprobe. I have proved that fluctuation correlation spectroscopy can be used to characterize fluorescent calcium probes such as Oregon Green Bapta 5N. I have also pointed out the limits of the method. I have enlightened and characterized an unexpected anisotropy of the two photon absorption and emission of the photoluminescence of gold nanospheres. Its interpretation stresses out the importance of the surface states and of the dynamics of the ligands. I have also studied nanoprobes made of a gold nanobead functionalized with chromophores. An original method, based on the hybrid nature of the probe, has been used to demonstrate the heterogeneity of such systems, fluorophore aggregates formation and the very strong quenching of the fluorescence of the chromophores linked to the gold nanoparticles.La spectroscopie de corrélation de fluctuation a été utilisée pour étudier la réponse optique, en solution, de molécules et de billes d'or nanométriques individuelles, fonctionnalisées ou non, en vue du développement de nouvelles sondes biochimiques. Les expériences réalisées s'appuient sur un système de microscopie confocale et/ou biphotonique optimisé pour la détection de faibles signaux. Plusieurs procédés de filtrage du signal de fluorescence et d'algorithmes de calcul de la corrélation ont permis une analyse détaillée des signaux acquis. A travers un modèle original, je montre qu'il faut tenir compte de la réponse impulsionnelle tensorielle du microscope lors de l'ajustement des courbes de corrélation de particules ayant un diagramme d'émission anisotrope. Je me suis intéressé à trois types de nanosondes différentes. J'ai montré que l'on peut caractériser efficacement des sondes calciques comme l'Oregon Green Bapta 5N par spectroscopie de corrélation de fluctuations tout en pointant les limites de la méthode. J'ai ensuite mis en évidence et caractérisé une anisotropie inattendue de l'absorption à deux photons et de l'émission de photoluminescence de nanosphères d'or. Son interprétation montre l'importance du rôle des états de surface et de celui des ligands et de leur dynamique. J'ai aussi caractérisé des nanosondes formées de particule d'or fonctionnalisées avec des chromophores. Une technique originale s'appuyant sur la nature hybride de la sonde, m'a permis de démontrer l'hétérogénéité de ces systèmes, la formation d'agrégats de fluorophores et la très forte annihilation de la fluorescence des chromophores liés aux particules d'or
Characterizing Jacobians via the KP equation and via flexes and degenerate trisecants to the Kummer variety: an algebro-geometric approach
No full textWe give completely algebro-geometric proofs of a theorem by T. Shiota, and of a theorem by I. Krichever, characterizing Jacobians of algebraic curves among all irreducible principally polarized abelian varieties. Shiota’s characterization is given in terms of the KP equation. Krichever’s characterization is given in terms of trisecant lines to the Kummer variety. Here we treat the case of flexes and degenerate trisecants. The basic tool we use is a theorem we prove asserting that the base locus of the linear system associated to an effective line bundle on an abelian variety is reduced. This result allows us to remove all the extra assumptions that were introduced in the theorems by the first author, C. De Concini, G.Marini, and O. Debarre, in order to achieve algebro-geometric proofs of the results above
Spectroscopie de nanosondes hybrides à coeur métallique
No full textFluctuation Correlation Spectroscopy has been used to characterize the optical response of molecules and individual gold nanobeads, in solution. The latter are functionalized or not, and are aimed to be used as new biochemical nanoprobes. All the experiments were carried on an optimized confocal or/and biphotonic microscope in order to detect very weak signals. Several filtering procedures of the fluorescence signal and correlation calculation algorithms were used to precisely analyze the data. I show that the impulsional tensorial response of the microscope has to be taken into account to fit the correlation curves of particles with an anisotropic emission diagram. I have studied three different kinds of nanoprobe. I have proved that fluctuation correlation spectroscopy can be used to characterize fluorescent calcium probes such as Oregon Green Bapta 5N. I have also pointed out the limits of the method. I have enlightened and characterized an unexpected anisotropy of the two photon absorption and emission of the photoluminescence of gold nanospheres. Its interpretation stresses out the importance of the surface states and of the dynamics of the ligands. I have also studied nanoprobes made of a gold nanobead functionalized with chromophores. An original method, based on the hybrid nature of the probe, has been used to demonstrate the heterogeneity of such systems, fluorophore aggregates formation and the very strong quenching of the fluorescence of the chromophores linked to the gold nanoparticles.La spectroscopie de corrélation de fluctuation a été utilisée pour étudier la réponse optique, en solution, de molécules et de billes d'or nanométriques individuelles, fonctionnalisées ou non, en vue du développement de nouvelles sondes biochimiques. Les expériences réalisées s'appuient sur un système de microscopie confocale et/ou biphotonique optimisé pour la détection de faibles signaux. Plusieurs procédés de filtrage du signal de fluorescence et d'algorithmes de calcul de la corrélation ont permis une analyse détaillée des signaux acquis. A travers un modèle original, je montre qu'il faut tenir compte de la réponse impulsionnelle tensorielle du microscope lors de l'ajustement des courbes de corrélation de particules ayant un diagramme d'émission anisotrope. Je me suis intéressé à trois types de nanosondes différentes. J'ai montré que l'on peut caractériser efficacement des sondes calciques comme l'Oregon Green Bapta 5N par spectroscopie de corrélation de fluctuations tout en pointant les limites de la méthode. J'ai ensuite mis en évidence et caractérisé une anisotropie inattendue de l'absorption à deux photons et de l'émission de photoluminescence de nanosphères d'or. Son interprétation montre l'importance du rôle des états de surface et de celui des ligands et de leur dynamique. J'ai aussi caractérisé des nanosondes formées de particule d'or fonctionnalisées avec des chromophores. Une technique originale s'appuyant sur la nature hybride de la sonde, m'a permis de démontrer l'hétérogénéité de ces systèmes, la formation d'agrégats de fluorophores et la très forte annihilation de la fluorescence des chromophores liés aux particules d'or
Kuznetsov's Fano threefold conjecture via K3 categories and enhanced group actions
No full textWe settle the last open case of Kuznetsov's conjecture on the derived
categories of Fano threefolds. Contrary to the original conjecture, we prove
the Kuznetsov components of quartic double solids and Gushel-Mukai threefolds
are never equivalent, as recently shown independently by Zhang. On the other
hand, we prove the modified conjecture asserting their deformation equivalence.
Our proof of nonequivalence combines a categorical Enriques-K3 correspondence
with the Hodge theory of categories. Along the way, we obtain a categorical
description of the periods of Gushel-Mukai varieties, which we use to resolve a
conjecture of Kuznetsov and the second author on the birational categorical
Torelli problem, as well as to give a simple proof of a theorem of Debarre and
Kuznetsov on the fibers of the period map. Our proof of deformation equivalence
relies on results of independent interest about obstructions to enhancing group
actions on categories.Comment: 42 pages, minor update
TV-based spline reconstruction with Fourier measurements: Uniqueness and convergence of grid-based methods
No full textWe study the problem of recovering piecewise-polynomial periodic functions from their low-frequency information. This means that we only have access to possibly corrupted versions of the Fourier samples of the ground truth up to a maximum cutoff frequency Kc. The reconstruction task is specified as an optimization problem with total-variation (TV) regularization (in the sense of measures) involving the Mth order derivative regularization operator L = DM. The order M >= 1 determines the degree of the reconstructed piecewise-polynomial spline, whereas the TV regularization norm, which is known to promote sparsity, guarantees a small number of pieces. We show that the solution of our optimization problem is always unique, which, to the best of our knowledge, is a first for TV-based problems. Moreover, we show that this solution is a periodic spline matched to the regularization operator L whose number of knots is upper-bounded by 2Kc. We then consider the grid-based discretization of our optimization problem in the space of uniform L-splines. On the theoretical side, we show that any sequence of solutions of the discretized problem converges uniformly to the unique solution of the gridless problem as the grid size vanishes. Finally, on the algorithmic side, we propose a B-spline-based algorithm to solve the discretized problem, and we demonstrate its numerical feasibility experimentally. On both of these aspects, we leverage the uniqueness of the solution of the original problem.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).LI
