The geometry of Ulrich bundles on del Pezzo surfaces


Coskun E. , Kulkarni R. S. , MUSTOPA Y.

JOURNAL OF ALGEBRA, vol.375, pp.280-301, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 375
  • Publication Date: 2013
  • Doi Number: 10.1016/j.jalgebra.2012.08.032
  • Title of Journal : JOURNAL OF ALGEBRA
  • Page Numbers: pp.280-301

Abstract

Given a smooth del Pezzo surface X-d subset of P-d of degree d, we isolate the essential geometric obstruction to a vector bundle on X-d being an Ulrich bundle by showing that an irreducible curve D of degree dr on X-d represents the first Chern class of a rank-r Ulrich bundle on X-d if and only if the kernel bundle of the general. smooth element of vertical bar D vertical bar admits a generalized theta-divisor. Moreover, we show that any smooth arithmetically Gorenstein surface whose Ulrich bundles admit such a characterization is necessarily del Pezzo.