Description
Title: Curve-Jacobian correspondence
Abstract: By the Riemann-Roch theorem, when m> 2g-2, the m-th symmetric product of a smooth projective curve is a projective bundle over its Jacobian. It is natural to ask whether this relationship extends to families of curves that may have singularities.
In this talk, I will describe a correspondence between algebraic cycles on the universal compactified Jacobians over the moduli space of stable curves and those on the moduli space of stable curves with additional markings. This correspondence allows one to transport structures between two sides. It brings together Fourier transforms, the P=C phenomenon, ring structures, logarithmic Abel-Jacobi theory, tautological relations, and many other aspects. This is a joint work in progress with A. Pixton.