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arXiv · 1510.08061

Extremality of loci of hyperelliptic curves with marked Weierstrass points

Dawei Chen·Nicola Tarasca
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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 genus-two 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.

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Dawei Chen, Nicola Tarasca. 2016-09-14. Extremality of loci of hyperelliptic curves with marked Weierstrass points. https://doi.org/10.2140/ant.2016.10.1935

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