A blowup formula for virtual Donaldson invariants

Nikolas Kuhn (Stanford University)

26-Mar-2021, 19:00-20:00 (2 years ago)

Abstract: 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.

algebraic geometry

Audience: researchers in the topic

( video )

Comments: The discussion for Nikolas Kuhn’s talk is taking place not in zoom-chat, but at tinyurl.com/2021-03-26-nk (and will be deleted after ~3-7 days).

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

Organizer: Ravi Vakil*
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