**
Kota Yoshioka
**

**Wall crossing formula for the Euler
characteristic
of determinant line bundles.
**

**Abstract
**

**
**
Let *M*_{H}(c_{1},c_{2}) be the moduli of
*H*-stable sheaves on a surface *X*.
For a divisor *D* on *X*, we can associate a determinant line bundle
whose first chern class is defined by the μ-map.
I consider the Euler characteristic of this determinant line bundle.In
particular, I will talk about the wall crossing formula under
a suitable assumption on *X*.
This is a joint work with Lothar Goettsche and Hiraku Nakajima.