TY - JOUR

T1 - A Clifford inequality for semistable curves

AU - Christ, Karl

N1 - Funding Information: The author was supported by the Israel Science Foundation (grant No. 821/16) and by the Center for Advanced Studies at BGU. Open Access funding enabled and organized by Projekt DEAL. Acknowledgments: Many discussions with Lucia Caporaso and Ilya Tyomkin helped shape this paper, and I am very grateful for the insights and suggestions they provided. In addition, I would like to thank Matt Baker, Sam Payne, Sara Torelli and an anonymous referee, whose comments on an earlier draft led to many improvements in presentation.

PY - 2023/1

Y1 - 2023/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85143603078&partnerID=8YFLogxK

U2 - 10.1007/s00209-022-03173-7

DO - 10.1007/s00209-022-03173-7

M3 - Article

AN - SCOPUS:85143603078

VL - 303

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 15

M1 - 15

ER -