1,721,291 research outputs found
Generic vanishing and minimal cohomology classes on abelian varieties
No full textWe establish a-and conjecture further-relationship between the existence of subvarieties representing minimal cohomology classes on principally polarized abelian varieties, and the generic vanishing of the cohomology of twisted ideal sheaves. The main ingredient is the Generic Vanishing criterion established in Pareschi G. and Popa M. (GV-sheaves, Fourier-Mukai transform, and Generic Vanishing. Preprint math.AG/0608127), based on the Fourier-Mukai transform
M-regularity and the fourier-mukai transform
No full textThis is a survey of M-regularity and its applications, expanding on lectures given by the second author at the Seattle conference, in August 2005, and at the Luminy workshop "Geometrie Algebrique Complexe", in October 2005
GV-sheaves, Fourier-Mukai transform, and generic vanishing
No full textWe use homological methods to establish a formal criterion for Generic Vanishing, in the sense originated by Green and Lazarsfeld and pursued further by Hacon and the first author, but in the context of an arbitrary Fourier-Mukai correspondence. For smooth projective varieties we apply this to deduce a Kodaira-type generic vanishing theorem for adjoint bundles of the form K_X + L with L a nef line bundle, and in fact a more general generic Nadel-type vanishing theorem for multiplier ideal sheaves. Still in the context of the Picard variety, the same method generates various other generic vanishing results, by reduction to standard vanishing theorems. We further use the formal criterion in order to address examples related to generic vanishing on higher rank moduli spaces (on curves and on some threefold Calabi-Yau fiber spaces)
Strong generic vanishing and a higher dimensional Calstelnuovo-de Franchis inequality
No full textWe extend to manifolds of arbitrary dimension the Castelnuovo-de Franchis inequality for surfaces. The proof is based on the theory of Generic Vanishing and higher regularity, and on the Evans-Griffith Syzygy Theorem in commutative algebra. Along the way we give a positive answer, in the setting of Kahler manifolds, to a question of Green-Lazarsfeld on the vanishing of higher direct images of Poincare' bundles. We indicate generalizations to arbitrary Fourier-Mukai transforms
Castelnuovo theory and the geometric Schottky problem
No full textWe prove and conjecture results which show that Castelnuovo theory in projective space has a close analogue for abelian varieties. This is related to the geometric Schottky problem: our main result is that a principally polarized abelian variety satisfies a precise version of the Castelnuovo Lemma if and only if it is a Jacobian. This result has a surprising connection to the Trisecant Conjecture. We also give a genus bound for curves in abelian varieties
Regularity on abelian varieties I
No full textWe introduce the notion of Mukai regularity (-regularity) for coherent sheaves on abelian varieties. The definition is based on the Fourier-Mukai transform, and in a special case depending on the choice of a polarization it parallels and strengthens the usual Castelnuovo-Mumford regularity. Mukai regularity has a large number of applications, ranging from basic properties of linear series on abelian varieties and defining equations for their subvarieties, to higher dimensional type statements and to a study of special classes of vector bundles. Some of these applications are explained here, while others are the subject of upcoming sequels
Regularity on abelian vaneties II: Basic results on linear series and defining equations
No full textWe apply the theory of M-regularity developed by the authors [Regularity on abelian varieties, I, J. Amer. Math. Soc. 16 (2003), 285-302] to the study of linear series given by multiples of ample line bundles on abelian varieties. We define an invariant of a line bundle, called M-regularity index, which governs the higher order properties and (partly conjecturally) the defining equations of such embeddings. We prove a general result on the behavior of the defining equations and higher syzygies in embeddings given by multiples of ample bundles whose base locus has no fixed components, extending a conjecture of Lazarsfeld [proved in Syzygies of abelian varieties, J. Amer. Math. Soc. 13 (2000), 651-664]. This approach also unifies essentially all the previously known results in this area, and is based on Fourier-Mukai techniques rather than representations of theta groups
Regularity on Abelian Varieties III: Relationship with Generic Vanishing and Applications
No full textWe describe the relationship between the notions of M-regular sheaf and GV-sheaf in the case of abelian varieties. The former is a natural strengthening of the latter, and we provide an algebraic criterion characterizing it among the larger class. Based on this we deduce new basic properties of both M-regular and GV-sheaves. In the second part we give a number of applications of generation criteria for M-regular sheaves to the study of Seshadri constants, Picard bundles, pluricanonical maps on irregular varieties, and semihomogeneous vector bundles. Thi
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
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