The locus of curves with an odd subcanonical point

Abstract

We present an explicit construction of a compactification of the locus of smooth curves whose symmetric Weierstrass semigroup at a marked point is odd. This construction extends Stöhr’s techniques, which can be seen as a variant of Hauser’s algorithm for computing versal deformation spaces. As an application, we prove the rationality of the locus for genus at most six.