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Mathematics > Algebraic Geometry

arXiv:2204.08234 (math)
[Submitted on 18 Apr 2022 (v1), last revised 1 Nov 2022 (this version, v2)]

Title:A Clifford inequality for semistable curves

Authors:Karl Christ
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Abstract:Let $X$ be a semistable curve and $L$ a line bundle whose multidegree is uniform, i.e., in the range between those of the structure sheaf and the dualizing sheaf of $X$. We establish an upper bound for $h^0(X,L)$, which generalizes the classic Clifford inequality for smooth curves. The bound depends on the total degree of $L$ and connectivity properties of the dual graph of $X$. It is sharp, in the sense that on any semistable curve there exist line bundles with uniform multidegree that achieve the bound.
Comments: Added Corollary 4.5 and Lemma 4.10, as well as some changes in presentation following a referee report. 19 pages, 4 Figures. Final version, to appear in Math. Z
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:2204.08234 [math.AG]
  (or arXiv:2204.08234v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2204.08234

Submission history

From: Karl Christ [view email]
[v1] Mon, 18 Apr 2022 09:46:17 UTC (24 KB)
[v2] Tue, 1 Nov 2022 09:49:12 UTC (27 KB)
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