UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

September 18, 2018

939 Evans Hall

3:45PM: Curves of genus 11 with several maps of degree 6 to P^1

Frank Schreyer

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 P^1.

5:00PM: Curves on surfaces with ordinary singularities in P^3

Mengyuan Zhang

We study curves in P3 lying on hypersurfaces that arise as images of “general” maps from smooth surfaces. We describe the numerical invariants of a large class of curves on these surfaces, and study the families of such curves in the Hilbert scheme.

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