Bounding cohomology on a smooth projective surface with Picard number 2

2020/07/25 by Li, Sichen
#14C20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.12855

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. When the Picard number ρ(X)=2, we prove that if either the Kodaira dimension κ(X)=1 and X has a negative curve or X has two negative curves, then this conjecture holds for X.

Related

• Bounding cohomology on a smooth projective surface
• Bounded cohomology property on a smooth projective surface with Picard number two
• Bounded cohomology property on smooth projective fibered surfaces
• Bounding Picard numbers of surfaces using p-adic cohomology
• Some surfaces with maximal Picard number