Logo

Mathematical Sciences Research Institute

Home » GT Program Seminar: Morse Theory on Moduli Spaces of Pairs and the Bogomolov-Miyaoka-Yau Inequality

Seminar

GT Program Seminar: Morse Theory on Moduli Spaces of Pairs and the Bogomolov-Miyaoka-Yau Inequality November 08, 2022 (11:00 AM PST - 12:00 PM PST)
Parent Program:
Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Paul Feehan (Rutgers University)
Description No Description
Video

GT Program Seminar: Morse Theory On Moduli Spaces Of Pairs And The Bogomolov-Miyaoka-Yau Inequality

Abstract/Media

To participate in this seminar, please register HERE.

We describe an approach to Bialynicki-Birula theory for holomorphic C^* actions on complex analytic spaces and Morse-Bott theory for Hamiltonian functions for the induced circle actions. A key principle is that positivity of a suitably defined "virtual Morse-Bott index" at a critical point of the Hamiltonian function implies that the critical point cannot be a local minimum. Inspired by Hitchin’s 1987 study of the moduli space of Higgs monopoles over Riemann surfaces, we apply our method in the context of the moduli space of non-Abelian monopoles or, equivalently, stable holomorphic pairs over a closed, complex, Kaehler surface. We use the Hirzebruch-Riemann-Roch Theorem to compute virtual Morse-Bott indices of all critical strata (Seiberg-Witten moduli subspaces) and show that these indices are positive in a setting motivated by a conjecture that all closed, smooth four-manifolds of Seiberg-Witten simple type (including symplectic four-manifolds) obey the Bogomolov-Miyaoka-Yau inequality.

Asset no preview Morse Theory on Moduli Spaces of Pairs and the Bogomolov-Miyaoka-Yau Inequality 851 KB application/pdf

GT Program Seminar: Morse Theory On Moduli Spaces Of Pairs And The Bogomolov-Miyaoka-Yau Inequality