# Finite subschemes of abelian varieties and the Schottky problem

Martin G. Gulbrandsen^{[1]}; Martí Lahoz^{[2]}

- [1] Stord/Haugesund University College, Bjørnsons gate 45 NO-5528 Haugesund (Norway)
- [2] Universitat de Barcelona Departament d’Àlgebra i Geometria Gran Via, 585, 08007 Barcelona (Spain)

Annales de l’institut Fourier (2011)

- Volume: 61, Issue: 5, page 2039-2064
- ISSN: 0373-0956

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topGulbrandsen, Martin G., and Lahoz, Martí. "Finite subschemes of abelian varieties and the Schottky problem." Annales de l’institut Fourier 61.5 (2011): 2039-2064. <http://eudml.org/doc/219804>.

@article{Gulbrandsen2011,

abstract = {The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians, among indecomposable principally polarized abelian varieties $(A, \Theta )$ of dimension $g$, by the existence of $g + 2$ points $\Gamma \subset A$ in special position with respect to $2\Theta $, but general with respect to $\Theta $, and furthermore states that such collections of points must be contained in an Abel-Jacobi curve. Building on the ideas in the original paper, we give here a self contained, scheme theoretic proof of the theorem, extending it to finite, possibly nonreduced subschemes $\Gamma $.},

affiliation = {Stord/Haugesund University College, Bjørnsons gate 45 NO-5528 Haugesund (Norway); Universitat de Barcelona Departament d’Àlgebra i Geometria Gran Via, 585, 08007 Barcelona (Spain)},

author = {Gulbrandsen, Martin G., Lahoz, Martí},

journal = {Annales de l’institut Fourier},

keywords = {Principally polarized abelian varieties; Jacobians; Schotty problem; finite schemes; Abel-Jacobi curves; principally polarized abelian varieties},

language = {eng},

number = {5},

pages = {2039-2064},

publisher = {Association des Annales de l’institut Fourier},

title = {Finite subschemes of abelian varieties and the Schottky problem},

url = {http://eudml.org/doc/219804},

volume = {61},

year = {2011},

}

TY - JOUR

AU - Gulbrandsen, Martin G.

AU - Lahoz, Martí

TI - Finite subschemes of abelian varieties and the Schottky problem

JO - Annales de l’institut Fourier

PY - 2011

PB - Association des Annales de l’institut Fourier

VL - 61

IS - 5

SP - 2039

EP - 2064

AB - The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians, among indecomposable principally polarized abelian varieties $(A, \Theta )$ of dimension $g$, by the existence of $g + 2$ points $\Gamma \subset A$ in special position with respect to $2\Theta $, but general with respect to $\Theta $, and furthermore states that such collections of points must be contained in an Abel-Jacobi curve. Building on the ideas in the original paper, we give here a self contained, scheme theoretic proof of the theorem, extending it to finite, possibly nonreduced subschemes $\Gamma $.

LA - eng

KW - Principally polarized abelian varieties; Jacobians; Schotty problem; finite schemes; Abel-Jacobi curves; principally polarized abelian varieties

UR - http://eudml.org/doc/219804

ER -

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