## Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Curves of genus 11 with several maps of degree 6 to $\mathbb P^1$

Seminar | September 18 | 3:45-4:45 p.m. | 939 Evans Hall

Frank-Olaf Schreyer, MSRI, Universität des Saarlandes

Department of Mathematics

Green's conjecture says that vanishing syzgies of a canonical curve is equivalent to the non-existence of certain linear series on the curve. Turning things around, we might hope that many syzygies imply the existence of many linear systems. In this talk I will survey our knowledge on syzygies of canonical curves and then report on work of Hanieh Keneshlou, who used this approach to study the scheme of curves of genus 11 with several maps of degree 6 to $\mathbb P^1$.

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