Higher rank Clifford indices of curves on a K3 surface

• Soheyla Feyzbakhsh ^[2] ; Chunyi Li ^[1]
  1. [1] University of Warwick

     University of Warwick

     Reino Unido

     
  2. [2] Imperial College, Reino Unido
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 3, 2021
• Idioma: inglés
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• Resumen

  • 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.