Complex curves of genus three, Kummer surfaces and Quillen metrics

Abstract

Let C be a smooth, complex, projective curve of genus 3. By choosing an unramified double covering of C, the Abel-Prym map yields an embedding of C into a Kummer surface K when C is non-hyperelliptic. We compute the Quillen metric on Open image in new window the determinant of the cohomologies of Open image in new window with respect to the metric on C induced from the flat Kahler metric on K. For the computation of the Quillen metric, we show the exact self-duality of the Heisenberg-invariant Kummer's quartic surfaces.