HUJI NT Seminar - Sam Grushevsky "Non-isomorphic smooth compactifications of moduli of cubic surfaces"

Mon, 04/04/202214:30-16:00
Abstract: The moduli space of smooth complex cubic surfaces can be seen, by the work of Allcock-Carlson-Toledo, as a ball quotient. Thus the moduli space has two natural compactifications, one via geometric invariant theory, and the other as Baily-Borel compactification of a ball quotient. These compactifications admit natural smooth resolutions: the Kirwan desingularization of the GIT quotient, and the toroidal compactification of the ball quotient. We show that while these smooth compactifications of the moduli of cubics have the same Betti numbers, they are not isomorphic or either K-equivalent. Based on joint work in progress with S. Casalaina-Martin, K. Hulek, R. Laza