A Clifford inequality for semistable curves

Karl Christ

Research output: Contribution to journalArticlepeer-review


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(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.

Original languageEnglish
Article number15
JournalMathematische Zeitschrift
Issue number1
StatePublished - 1 Jan 2023

ASJC Scopus subject areas

  • Mathematics (all)


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