The geometry of Ulrich bundles on del Pezzo surfaces


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

JOURNAL OF ALGEBRA, cilt.375, ss.280-301, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

Özet

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.