The rationality of some moduli spaces of plane curves
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.
We describe the set of points over which a dominant polynomial map is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by .
We study the group of tame automorphisms of a smooth affine -dimensional quadric, which we can view as the underlying variety of . We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in is linearizable, and that satisfies the Tits alternative.