Supermeasure on moduli of supercurves

Abstract: This is a report on joint work with Giovanni Felder and David Kazhdan. I will discuss the moduli space of supercurves and its compactification, the moduli of stable supercurves. As in the classical case, the analog of Mumford’s isomorphism gives an expression of the canonical bundle on this moduli space in terms of the Berezinian of the Hodge bundle. We consider the corresponding supermeasure obtained from this isomorphism together with the natural hermitian metric on the Hodge bundle. Our main results concern its polar behaviour at infinity and on the null-theta divisor.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar