Algebraic surfaces with zero-dimensional cohomology support locus

2017/02/16 by Botong Wang, Wang, Botong · 2 citations
Mathematics · #14J80 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1702.05169

openalex publication_date 2017/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Transformation de Fourier generalisee

Cited by

• Generic vanishing for semi-abelian varieties and integral Alexander modules
• Mellin transformation, propagation, and abelian duality spaces

Related

• The Bloch conjecture
• On the cohomology of surfaces with p_g = q = 2 and maximal Albanese dimension
• Cohomological support loci of varieties of Albanese fiber dimension one
• On the cohomology of Stover Surface
• The basepoint-freeness threshold of a very general abelian surface