Dennis Eriksson: Theta functions, discriminants, and Riemann-Roch

Mumford has shown, using a version of the Riemann–Roch theorem, that certain line bundles associated to a family of curves are isomorphic. The equality of line bundle classes can be seen as a special form of a tautological relation, and the isomorphism is fundamental in arithmetic intersection theory. The isomorphism is however abstract, in the sense that it is deduced from the geometry of the moduli space of curves. 

In this talk I will give the background on the above material, and show that this relation can be described concretely by classical theta functions (nullwerte) and discriminants of polynomials, and offer some applications. This is joint work with Gerard Freixas i Montplet.