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Castelnuovo theory and the geometric Schottky problem

Giuseppe Pareschi·Mihnea Popa
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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.

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Giuseppe Pareschi, Mihnea Popa. 2007-06-26. Castelnuovo theory and the geometric Schottky problem. https://arxiv.org/abs/math/0407370

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