On Frobenius-destabilized rank-2 vector bundles over curves

  • Herbert Lange

    Universität Erlangen-Nünberg, Germany
  • Christian Pauly

    Université de Montpellier II, France

Abstract

Let be a smooth projective curve of genus over an algebraically closed field of characteristic . Let be the moduli space of semistable rank-2 vector bundles over with trivial determinant. The relative Frobenius map induces by pull-back a rational map . In this paper we show the following results.

  1. For any line bundle over , the rank- vector bundle is stable.
  2. The rational map has base points, i.e., there exist stable bundles over such that is not semistable.
  3. Let denote the scheme-theoretical base locus of . If , and ordinary, then is a 0-dimensional local complete intersection of length and the degree of equals .

Cite this article

Herbert Lange, Christian Pauly, On Frobenius-destabilized rank-2 vector bundles over curves. Comment. Math. Helv. 83 (2008), no. 1, pp. 179–209

DOI 10.4171/CMH/122