2016/07/22 by Yusuf Mustopa, Mustopa, Yusuf
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.1607.06550
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.