We 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.
Pareschi, G., Popa, M. (2008). Castelnuovo theory and the geometric Schottky problem. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 615(615), 25-44 [10.1515/CRELLE.2008.008].
Castelnuovo theory and the geometric Schottky problem
PARESCHI, GIUSEPPE;
2008-01-01
Abstract
We 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.File in questo prodotto:
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