A syzygy day
October 11, 2023University of TübingenA one-day workshop on syzygies of projective varieties and related topics. Talks by:
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© Location
The talks will take place in
- IFIB, Auf der Morgenstelle 32-34, Room 2T26.
The campus is most conveniently reached by bus. The bus stop is called BG Unfallklinik.
Schedule
11:15 - 12:15: Jinhyung Park.
12:15 - 14:00: Lunch break.
14:00 - 15:00: Gavril Farkas.
15:00 - 15:45: Coffee Break (in the Hermann Hankel room of building C4)
15:45 - 16:45: Frank-Olaf Schreyer.
Abstracts
Gavril Farkas. The Minimal Resolution Conjecture on points on generic curves
The Minimal Resolution Conjecture predicts the shape of the resolution of general sets of points on a projective variety in terms of the geometry of the variety. We present an essentially complete solution to this problem for general curves. Our methods also provide a proof (valid in arbitrary characteristic) of Butler's Conjecture on the stability of syzygy bundles on a general curve of every genus at least 3, as well as of the Frobenius semistability in positive characteristic of the syzygy bundle of a general curve in the range d>2r-1. Joint work with Eric Larson.
Jinhyung Park. Syzygies of secant varieties of smooth projective curves
In this talk, I report recent progress on syzygies of secant varieties of smooth projective curves obtained by joint work with Lawrence Ein and Wenbo Niu and joint work with Junho Choe and Sijong Kwak. First, we extend Green's (2g+1+p)-theorem to secant varieties of smooth projective curves. This confirms Sidman-Vermeire's conjecture. Next, we show a generalization of the gonality conjecture on syzygies of smooth projective curves to their secant varieties. More precisely, we prove that the gonality sequence of a smooth projective curve completely determines the shape of the minimal free resolutions of secant varieties of curves of large degree. This answers a question of Ein. Our results show that there is a "matryoshka structure'' among secant varieties of smooth projective curves.
Frank-Olaf Schreyer. Hyperelliptic Curves and Ulrich sheaves on the complete intersection of two quadrics
Using the connection between hyperelliptic curves, Clifford algebras, and complete intersections X of two quadrics, we describe Ulrich bundles on X and construct some of minimal possible rank. This is joint work with David Eisenbud based in part on unpublished work with our dear friend the late Ragnar Buchweitz.