Nikolas Kuhn (March 26, 2021):  A blowup formula for virtual Donaldson invariants
Channel: Algebraic Geometry at Stanford
Date: 2021-04-16

Donaldson invariants were a breakthrough in the study of smooth four-manifolds when they were introduced in the 1980s and even found applications to the classification of compact complex surfaces. With the advent of the virtual fundamental class, it has become possible to give an elegant purely algebraic definition when working on a complex projective surface X, which was done by T. Mochizuki. The two definitions agree in most cases, and whether they agree in general comes down to knowing a blowup formula for Mochizuki's invariants. We present a direct proof of such a blowup formula that generalizes earlier results by Göttsche-Nakajima-Yoshioka and has applications to other types of enumerative invariants of X. This is joint work with Yuuji Tanaka.