scholarly journals Finite subschemes of abelian varieties and the Schottky problem

2011 ◽  
Vol 61 (5) ◽  
pp. 2039-2064 ◽  
Author(s):  
Martin G. Gulbrandsen ◽  
Martí Lahoz
Keyword(s):  
Abelian Varieties ◽  
Schottky Problem

Algebraic and rigid geometry on the Schottky problem

2015 ◽  
Vol 2015 (705) ◽  
Author(s):  
Takashi Ichikawa
Keyword(s):  
Abelian Varieties ◽  
Theta Functions ◽  
Jacobian Varieties ◽  
Schottky Problem

AbstractWe study the Schottky problem by giving the KP characterization of Jacobian varieties among abelian varieties in terms of their algebraic or nonarchimedean theta functions.

scholarly journals Semicontinuity of Gauss maps and the Schottky problem

2021 ◽  
Author(s):  
Giulio Codogni ◽  
Thomas Krämer
Keyword(s):  
Abelian Variety ◽  
Moduli Space ◽  
Cotangent Bundle ◽  
Abelian Varieties ◽  
Topological Type ◽  
Intersection Cohomology ◽  
Theta Divisor ◽  
Schottky Problem ◽  
Gauss Maps

AbstractWe show that the degree of Gauss maps on abelian varieties is semicontinuous in families, and we study its jump loci. As an application we obtain that in the case of theta divisors this degree answers the Schottky problem. Our proof computes the degree of Gauss maps by specialization of Lagrangian cycles on the cotangent bundle. We also get similar results for the intersection cohomology of varieties with a finite morphism to an abelian variety; it follows that many components of Andreotti–Mayer loci, including the Schottky locus, are part of the stratification of the moduli space of ppav’s defined by the topological type of the theta divisor.

scholarly journals Characteristic cycles and the microlocal geometry of the Gauss map, II

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas Krämer
Keyword(s):  
Weak Solution ◽  
Weyl Group ◽  
Lie Algebras ◽  
Abelian Variety ◽  
Cotangent Bundle ◽  
Abelian Varieties ◽  
Gauss Map ◽  
Schottky Problem ◽  
Group Orbit

Abstract We show that any Weyl group orbit of weights for the Tannakian group of semisimple holonomic 𝒟 {{\mathscr{D}}} -modules on an abelian variety is realized by a Lagrangian cycle on the cotangent bundle. As applications we discuss a weak solution to the Schottky problem in genus five, an obstruction for the existence of summands of subvarieties on abelian varieties, and a criterion for the simplicity of the arising Lie algebras.

Analytic Theory of Abelian Varieties

1974 ◽  
Author(s):  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Abelian Varieties ◽  
Analytic Theory

scholarly journals Classification of nonrigid families of abelian varieties

1993 ◽  
Vol 45 (2) ◽  
pp. 159-189
Author(s):  
Masa-Hiko Saitō
Keyword(s):  
Abelian Varieties

scholarly journals Some results about the projective normality of abelian varieties

2005 ◽  
Vol 85 (5) ◽  
pp. 409-418 ◽  
Author(s):  
Luis Fuentes García
Keyword(s):  
Abelian Varieties ◽  
Projective Normality

scholarly journals Lifting automorphisms on Abelian varieties as derived autoequivalences

2021 ◽  
Author(s):  
Tanya Kaushal Srivastava
Keyword(s):  
Abelian Varieties

Very ample line bundles on quasi-abelian varieties

2001 ◽  
Vol 236 (1) ◽  
pp. 191-200 ◽  
Author(s):  
Shigeharu Takayama
Keyword(s):  
Abelian Varieties ◽  
Line Bundles
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