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Inside the moduli space of curves of genus three with one marked point, weconsider the locus of hyperelliptic curves with a marked Weierstrass point, andthe locus of non-hyperelliptic curves with a marked hyperflex. These loci havecodimension two. We compute the classes of their closures in the moduli spaceof stable curves of genus three with one marked point. Similarly, we computethe class of the closure of the locus of curves of genus four with an eventheta characteristic vanishing with order three at a certain point. These locinaturally arise in the study of minimal strata of Abelian differentials.

Loci of curves with subcanonical points in low genus