The geometry of Ulrich bundles on del Pezzo surfaces

Coşkun, Emre
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.


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