English

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.

Keywords

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}
}
R2 v1 2026-06-22T18:20:45.549Z