The geometry of Ulrich bundles on del Pezzo surfaces

Coşkun, Emre
Kulkarni, Rajesh S.
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.

Citation Formats
E. Coşkun, R. S. Kulkarni, and Y. MUSTOPA, “The geometry of Ulrich bundles on del Pezzo surfaces,” JOURNAL OF ALGEBRA, vol. 375, pp. 280–301, 2013, Accessed: 00, 2020. [Online]. Available: