Extremality of Loci of Hyperelliptic Curves with Marked Weierstrass Points

Abstract. The locus of genus-two curves with n marked Weierstrass points has codimension n inside the moduli space of genus-two curves with n marked points, for n ≤ 6. It is well known that the class of the closure of the divisor obtained for n = 1 spans an extremal ray of the cone of effective divisor classes. We generalize this result for all n: we show that the class of the closure of the locus of genustwo curves with n marked Weierstrass points spans an extremal ray of the cone of effective classes of codimension n, for n ≤ 6. A related construction produces extremal nef curve classes in moduli spaces of pointed elliptic curves.