# Algebraic Geometry Seminar

#### Canonical surfaces whose resolutions have big cotagent bundle

**Speaker:**
Bruno de Oliveira

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, May 7, 2019, 3:30 p.m.

**Synopsis:**

Surfaces with big cotangent bundle have hyperbolic properties. If $X$ is

of general type this is guaranteed if the 2nd Segre class is positive.

When the 2nd Segre class is negative or maybe better when the quotient

$c_1^2/c_2<1$ few examples are known with big cotangent bundle.

In a previous work with Bogomolov we showed that there are surfaces with

$c_1^2/c_2$ as low as $27/41$ with big cotangent bundle using resolutions

of nodal hypersurfaces. Our approach was repackaged by Rousseau-Rolleau in

a general form by stating that a canonical surface for which the sum of

the 2nd Segre class of the minimal resolution with the orbifold 2nd Segre

class is positive has the minimal resolution has a big cotangent bundle.

In this talk we improve on our previous result and hence also

Rosseau-Rolleau. Using a study on how canonical singularities impact h^1,

we obtain a better criterion to have big cotangent bundle and obtain

surfaces with $c_1^2/c_2=8/19$ with big cotangent bundle. Joint work with

Michael Weiss.