The geometry of Ulrich bundles on del Pezzo surfaces

Date

2013-02-01

Author

Coşkun, Emre
Kulkarni, Rajesh S.
MUSTOPA, Yusuf

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Subject Keywords

Ulrich bundles, Algebraic surfaces

URI

https://hdl.handle.net/11511/39148

Collections

Department of Mathematics, Article