The rationality of some moduli spaces of plane curves
We show that every local polynomial diffeomorphism (f,g) of the real plane such that deg f ≤ 3, deg g ≤ 3 is a global diffeomorphism.
We review a construction of Ellingsrud-Strømme relating instantons of charge n on the ordinary projective space and theta-characteristics on a plane curve of degree n with some extra-structure.
The Schottky-Jung proportionality theorem, from which the Schottky relation for theta functions follows, is proved for Mumford curves, i.e. curves defined over a non-archimedean valued field which are parameterized by a Schottky group.