Bernd Ulrich

ABSTRACT

The Behrend function is a constructible integer valued function defined on any scheme of finite type over the complex numbers. It plays an important role in the treatment of enumerative invariants in Donaldson-Thomas theory. But even in simple cases, the Behrend function is notoriously difficult to compute. In this talk we focus on zero-dimensional schemes, where we determine the Behrend function in many situations. Our methods are from commutative algebra, and involve blowup algebras, Rees valuations, and Newton polyhedra.

This is joint work with Alessio Sammartano and Claudia Polini.