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June, 2018 Algebraic Surfaces with Zero-dimensional Cohomology Support Locus
Botong Wang
Taiwanese J. Math. 22(3): 607-614 (June, 2018). DOI: 10.11650/tjm/170808


Using the theory of cohomology support locus, we give a necessary condition for the Albanese map of a smooth projective surface to be a submersion. More precisely, assuming that 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.


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Botong Wang. "Algebraic Surfaces with Zero-dimensional Cohomology Support Locus." Taiwanese J. Math. 22 (3) 607 - 614, June, 2018.


Received: 2 March 2017; Revised: 16 August 2017; Accepted: 22 August 2017; Published: June, 2018
First available in Project Euclid: 14 October 2017

zbMATH: 06965387
MathSciNet: MR3807327
Digital Object Identifier: 10.11650/tjm/170808

Primary: 14J80

Keywords: Albanese map , algebraic surfaces , cohomology support loci

Rights: Copyright © 2018 The Mathematical Society of the Republic of China


Vol.22 • No. 3 • June, 2018
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