Unirationality of Hurwitz Spaces and Existence of Ulrich Bundles
Vortrag von Dr. Florian Geiss
Datum: 14.05.12 Zeit: 13.15 - 14.00 Raum: Y27H25
The unirationality of Hurwitz spaces of d-gonal curves of all genera g>=d-1 is classical for d<=5. We give a computer-aided proof of the unirationality of Hurwitz spaces of 6-gonal curves for most values of g<=45. We also present an application of this construction to the existence of Ulrich bundles, i.e. arithmetically Cohen-Macaulay bundles on a projective variety X that have the maximum number of generators of the associated graded module. We give a short overview of the mathematical context and outline the proof of existence of stable Ulrich bundles of any rank r>=2 on a general cubic threefold. The latter is based on work of M. Casanellas and R. Hartshorne and joined work with F.-O. Schreyer.