1,721,070 research outputs found
Edge volume: 2018–2022
No full textPreface to the volume dedicated to Edge conferences from 2018 to 202
Flexibility Properties in Complex Analysis and Affine Algebraic Geometry
No full textIn the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
On slope stability of tangent sheaves on smooth toric Fano varieties
Get PDFWe prove that number 82 in the Batyrev-Sato classi cation of smooth toric Fano
4-folds is an explicit counterexample of Picard rank 4 to a long-standing conjecture due to Peternell - the fi rst known counterexample of Picard rank greater
than 1. Speci cally, we use toric methods to show that the tangent sheaf admits
exactly one equivariant destabilizing subsheaf and that this subsheaf is not the
relative tangent sheaf of any (not necessarily elementary) Mori bration. We give
the classification of the 124 smooth toric Fano 4-folds according to stability of
their tangent bundles, provide the Harder-Narasimhan filtrations in all 74 cases
in which the tangent bundle is unstable, and show that number 82 is the only
counterexample to Peternell's conjecture among the smooth toric Fano 4-folds.
There are 3 other cases in which none of the terms of the Harder-Narasimhan
fi ltration come from a Mori bration, 2 of which are blow-downs of number 82,
and we examine these 3 in some detail. We fi nish with some observations and
conjectures to do with stability of the tangent bundle on Fano Bott towers, and
an appendix containing Macaulay2 code which can be used to compute stability
and Harder-Narasimhan fi ltrations of tangent sheaves on toric varieties
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Fano varieties: positivity, K-stability and more
Get PDFThis thesis is about Fano varieties and their properties. We will determine the
K-stability of certain singular del Pezzo surfaces and smooth Fano 3-folds, the
existence of cylinders in singular del Pezzo surfaces, and also classify higher dimensional Fano varieties with certain properties. In dimension 2, many new
examples of K-stable polarized singular del Pezzo surfaces with du Val singular
points have been introduced and the existence of polarized cylinders in many
of these surfaces has been determined. We also completely solve the K- stability problem for singular del Pezzo surfaces that are index 2 hypersurfaces in
weighted projective space. In dimension 3, all deformation families of smooth
three-dimensional Fano varieties that contain K-polystable elements have been
described. In higher dimensions, a complete classification of smooth Fano varieties of large index that have positive second and third Chern characters has
been given, and all rational homogeneous spaces of Picard rank 1 having positive second Chern character have been described. In particular, we prove that
the only rational homogeneous spaces of Picard rank 1 with positive second and
third Chern characters are projective spaces and quadric hypersurfaces. This
thesis also contains few auxiliary results, which are closely related to K- stability
of Fano varieties. For instance, for a reduced plane curve of degree d, the sixth
worst log canonical threshold that it can have, has been determined
Birational geometry of Fano fibrations
No full textAn algebraic variety is called rationally connected if two generic points can be connected by a curve isomorphic to the projective line. The output of the minimal model program applied to rationally connected variety is variety admitting Mori fiber spaces over a rationally connected base. In this thesis we study the birational geometry of a particular class of rationally connected Mori fiber spaces: Fano fibrations over the projective line. We construct examples of Fano fibrations with a unique Mori fiber space in their birational classes. We prove that these examples are not birational to varieties of Fano type, thus answering the question of Cascini and Gongyo. That is we prove that the classes of rationally connected varieties and varieties of Fano type are not birationally equivalent. To construct the examples we use the techniques of birational rigidity. A Mori fiber space is called birationally rigid if there is a unique Mori fiber space structure in its birational class. The birational rigidity of smooth varieties admitting a del Pezzo fibration of degrees 1 and 2 is a well studied question. Unfortunately it is not enough to study smooth del Pezzo fibrations as there are fibrations which do not have smooth or even smoothable minimal models. In the case of fibrations of degree 2 we know that there is a minimal model with 2-Gorenstein singularities. These singularities are degenerations of the simplest terminal quotient singularity: singular points of the type 1/2(1,1,1). We give first examples of birationally rigid del Pezzo fibrations with 2-Gorenstein singularities. We then apply this result to study finite subgroups of the Cremona group of rank three. We then study the birational geometry of Fano fibrations from a different side. Using the reduction to characteristic 2 method we prove that double covers of Pn-bundles over Pm branched over a divisor of sufficiently high degree are not stably rational. For a del Pezzo fibration Y→P1 of degree 2 such that X is smooth there is a double cover Y→ X, where X is a P2-bundle over P1. In this case a stronger result holds: a very general Y with Pic(Y)≅Z⊕Z is not stably rational. We discuss the proof of this statement
Fano threefolds and algebraic families of surfaces of Kodaira dimension zero
Get PDFThe thesis consists of four chapters. First chapter is introductory. In Chapter 2, we recall some basic facts from the singularity theory of algebraic varieties (see Section
2.2) and the theory of minimal models (see Section 2.3), which will be used throughout the rest of
the thesis. We also make some conventions on the notions and notation used in the thesis (see
Section 2.1).
Each Chapter 3 and 4 starts with some preliminary results (see Sections 3.1 and 4.1, respectively).
Each Chapter 3 and 4 ends with some corollaries and conclusive remarks (see Sections 3.7 and 4.4, respectively).
In Chapter 3, we prove Theorem 1.2.7, providing the complete description of Halphen pencils on a
smooth projective quartic threefold X in P4. Let M be such a pencil. Firstly, we show that M ⊂ |
− nKX | for some n ∈ N, and
the pair (X,1n M) is canonical but not terminal. Further, if the set of not terminal centers CS(X, 1 ) (see Remark 2.2.8) does not contain points, we show that n = 1 (see Section 3.2). Finally, if there is a point P ∈ CS(X, n M), in Section 3.1 we show first that a general M ∈ M has multiplicity 2n at P (cf. Example 1.2.3). After that, analyzing the shape of the Hessian of the equation of X at
the point P , we prove that n = 2 and M coincides with the exceptional Halphen pencil from Example
1.2.6 (see Sections 3.3–3.6). In Chapter 4, we prove Theorem 1.2.11, which shows, in particular, that a general smooth K3 surfaces of type R is an anticanonical section of the Fano threefold X with canonical Gorenstein singularities and genus 36. In Section 4.2, we prove that X is unique up to an isomorphism and has
a unique singular point, providing the geometric quotient construction of the moduli
space F in Section 4.3 (cf. Remark 1.2.12). Finally, in Section 4.3 we prove that the forgetful map F −→ KR is generically surjective
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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