Bounding cohomology on a smooth projective surface

2018/05/28 by Sichen Li, Li, Sichen
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1805.10741

Abstract

The following conjecture arose out of discussions between B. Harbourne, J. Roé, C. Cilberto and R. Miranda: for a smooth projective surface X there exists a positive constant c_X such that h¹(\mathcal O_X(C))≤ c_X h⁰(\mathcal O_X(C)) for every prime divisor C on X. We show that the conjecture is true for some smooth projective surfaces with Picard number 2.

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