# Algebraic Geometry Seminar

#### Hyperplane Sections of K3 Surfaces

**Speaker:**
Enrico Arbarello, University of Rome

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, November 15, 2016, 3:10 p.m.

**Synopsis:**

In a series of recent papers with a combination of the following authors: Bruno (B), Sernesi (Se), Farkas (F) and Saccà (Sà), we study hyperplane sections of K3 surfaces and of limits thereof. The talk is an overview of these results. In '94 Wahl conjectured that a genus g, Brill-Noether-Petri canonical curve C is the hyperplane section of a K3 surface S in P^{g} if and only if the Gauss-Wahl map for C is non-surjective. In [ABSe] we prove this conjecture allowing S to be, possibly, a limit of K3 surfaces. In [ABFSà] and in [AB], by studying du Val curves, we prove that, indeed, this is the correct statement for the conjecture. Du Val curves also provide a negative answer to a well known question raised by Harris and Morrison in '98.