# Algebraic Geometry Seminar

#### Quadrics and Twisted Symmetric Differentials

**Speaker:**
Bruno de Oliveira, University of Miami

**Location:**
Warren Weaver Hall 905

**Date:**
Thursday, November 5, 2015, 3 p.m.

**Synopsis:**

Let X be a subvariety of ^{P}N. We will discuss a joint work with Prof. Bogomolov on the geometric meaning of sections of the symmetric powers of sheaf of differentials tensored by the line bundle O(1). There is no hope to have a precise geometric interpretation unless the codimension of X is low (dim X>2/3(N-1)). But if the codimension is low, then we will show how the space of these twisted symmetric differentials is related to the space of quadrics containing X. Using the same geometric framework we will reprove, if time permits, the vanishing of H^{0}(X,S^{m}Ω^{1}_{X}⊗ O(k)) if dim X>N/2 and m>k.