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Finite subschemes of abelian varieties and the schottky problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2011 (English)In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 61, no 5, 2039-2064 p.Article in journal (Refereed) Published
Abstract [en]

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 of 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.

Place, publisher, year, edition, pages
2011. Vol. 61, no 5, 2039-2064 p.
Keyword [en]
Abel-Jacobi curves, Finite schemes, Jacobians, Principally polarized abelian varieties, Schotty problem
National Category
URN: urn:nbn:se:kth:diva-152127DOI: 10.5802/aif.2665ISI: 000303946500009ScopusID: 2-s2.0-84858956032OAI: diva2:749472

QC 20140924

Available from: 2014-09-24 Created: 2014-09-23 Last updated: 2014-09-24Bibliographically approved

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Gulbrandsen, Martin G.
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