## EVENT DETAILS AND ABSTRACT

**Colloquium**
**Title:** Geometry and syzygies of algebraic curves

**Speaker:** Robert Lazarsfeld

**Speaker Info:** Stony Brook

**Brief Description:**

**Special Note**:

**Abstract:**

It is a classical theorem that if X is a Riemann surface of genus g, and if X is embedded in projective space in a sufficiently positive manner, then X is cut out by equations of degree 2. Mark Green realized in the early 1980s that one should see this as the first case of a more general picture involving higher syzygies. Around that time, he and I conjectured that one should be able to read off the "gonality" of X -- i.e. the least degree with which X can be expressed as a branched covering of the sphere -- from the resolution of the homogeneous ideal of X with respect to any one sufficiently positive embedding. Lawrence Ein and I recently noticed that this gonality conjecture in fact follows very simply from a small variant of ideas introduced by Voisin. In this talk aimed at non specialists, I will survey this circle of ideas.

**Date:** Wednesday, February 25, 2015

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Mihnea Popa

**Contact email:** mpopa@math.northwestern.edu

**Contact Phone:**

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