schottky problem
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Author(s):  
Giulio Codogni ◽  
Thomas Krämer

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.


2021 ◽  
pp. 358-373
Author(s):  
Hershel M. Farkas ◽  
Samuel Grushevsky ◽  
Riccardo Salvati Manni

Author(s):  
Thomas Krämer

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.


2019 ◽  
Vol 62 (11) ◽  
pp. 2211-2228
Author(s):  
Lizhen Ji
Keyword(s):  

2015 ◽  
Vol 365 (3-4) ◽  
pp. 1017-1039 ◽  
Author(s):  
Stefan Schreieder
Keyword(s):  

Author(s):  
Takashi Ichikawa

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.


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

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