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arXiv · 1805.10741

Bounding cohomology on a smooth projective surface

Sichen Li
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Abstract

The following conjecture arose out of discussions between B. Harbourne, J. Ro\'e, C. Cilberto and R. Miranda: for a smooth projective surface $X$ there exists a positive constant $c_X$ such that $h^1(\mathcal O_X(C))\le c_X h^0(\mathcal O_X(C))$ 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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Sichen Li. 2018-05-28. Bounding cohomology on a smooth projective surface. https://arxiv.org/abs/1805.10741

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