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arXiv · 1607.06550

Castelnuovo-Mumford Regularity and GV-Sheaves on Irregular Varieties

Yusuf Mustopa
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Abstract

Inspired by Beauville's recent construction of Ulrich sheaves on abelian surfaces, we pose the question of whether a torsion-free sheaf on a polarized smooth projective variety with Castelnuovo-Mumford regularity 1 is a GV (generic vanishing) sheaf, and present evidence that this question is governed by the positivity of cycles on generalized Brill-Noether loci. We prove that it has an affirmative answer for natural polarizations on many well-known irregular surfaces, as well as some polarizations on ruled threefolds over a curve.

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Yusuf Mustopa. 2016-07-22. Castelnuovo-Mumford Regularity and GV-Sheaves on Irregular Varieties. https://arxiv.org/abs/1607.06550

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