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Higher rank Clifford indices of curves on a K3 surface
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Feyzbakhsh, Soheyla and Li, Chunyi (2021) Higher rank Clifford indices of curves on a K3 surface. Selecta Mathematica, New Series, 27 . 48. doi:10.1007/s00029-021-00664-z ISSN 1022-1824.
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Official URL: https://doi.org/10.1007/s00029-021-00664-z
Abstract
Let (X,H) be a polarized K3 surface with Pic(X)=ZH, and let C∈|H| be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when g≥r2≥4, the rank r Clifford index of C can be computed by the restriction of Lazarsfeld-Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree d(≥5) smooth plane curve is d−4, which is the same as the Clifford index of the curve.
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||
Library of Congress Subject Headings (LCSH): | Clifford algebras , Curves on surfaces, Surfaces | |||||||||||||||
Journal or Publication Title: | Selecta Mathematica, New Series | |||||||||||||||
Publisher: | Birkhauser Verlag AG | |||||||||||||||
ISSN: | 1022-1824 | |||||||||||||||
Official Date: | 14 June 2021 | |||||||||||||||
Dates: |
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Volume: | 27 | |||||||||||||||
Article Number: | 48 | |||||||||||||||
DOI: | 10.1007/s00029-021-00664-z | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Date of first compliant deposit: | 7 June 2021 | |||||||||||||||
Date of first compliant Open Access: | 7 June 2021 | |||||||||||||||
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