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Mathematics > Algebraic Geometry

arXiv:1805.10741 (math)
[Submitted on 28 May 2018 (v1), last revised 12 Feb 2020 (this version, v8)]

Title:Bounding cohomology on a smooth projective surface

Authors:Sichen Li
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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 $h^1(\mathcal O_X(C))\le c_X h^0(\mathcal O_X(C))$ for every prime divisor $C$ on $X$. We show that the conjecture is true for some smooth projective surfaces with Picard number 2.
Comments: 11 pages
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1805.10741 [math.AG]
  (or arXiv:1805.10741v8 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.10741

Submission history

From: Sichen Li [view email]
[v1] Mon, 28 May 2018 02:35:50 UTC (11 KB)
[v2] Tue, 29 May 2018 14:00:36 UTC (11 KB)
[v3] Sun, 21 Oct 2018 06:44:05 UTC (10 KB)
[v4] Sun, 24 Feb 2019 04:19:16 UTC (1 KB) (withdrawn)
[v5] Thu, 13 Jun 2019 13:59:56 UTC (10 KB)
[v6] Sat, 17 Aug 2019 01:16:47 UTC (12 KB)
[v7] Fri, 22 Nov 2019 02:01:06 UTC (12 KB)
[v8] Wed, 12 Feb 2020 13:24:15 UTC (12 KB)
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