Algebraic surfaces with zero-dimensional cohomology support locus
Algebraic Geometry
2017-02-20 v1
Abstract
Using the theory of cohomology support locus, we give a necessary condition for the Albanese map of a smooth projective surface being a submersion. More precisely, assuming the cohomology support locus of any finite abelian cover of a smooth projective surface consists of finitely many points, we prove that the surface has trivial first Betti number, or is a ruled surface of genus one, or is an abelian surface.
Cite
@article{arxiv.1702.05169,
title = {Algebraic surfaces with zero-dimensional cohomology support locus},
author = {Botong Wang},
journal= {arXiv preprint arXiv:1702.05169},
year = {2017}
}