Higher-dimensional analogues of stable curves and of MMM invariants

Tuesday, 28-May-2024 

Abstract

The enumerative geometry of the moduli spaces of curves, which began in the 1980s with a famous paper of Mumford, is now an extremely developed field, with perhaps thousands of papers dedicated to it. Some highlights: MMM (Morita-Miller-Mumford) classes, Mumford's conjecture (Madsen-Weiss theorem), Witten's conjecture (Kontsevich's theorem), Gromov-Witten invariants.  After reviewing this "one-dimensional" case, I will explain some "higher-dimensional" generalizations: KSBA spaces of stable surfaces and higher-dimensional varieties, kappa classes on them, "higher" Gromov-Witen invariants, etc.