Harris and Morrison construct semistable families of k-gonal curves of genus g such that for every k the corresponding modular curves give a sweeping family in the k-gonal locus of the moduli space. Their construction depends on the choice of a smooth curve X. We show that if the genus g(X) is sufficiently high with respect to g then the geographical slope is 8 asymptotically with respect to g(X). Moreover, if some conjectured estimates given by Harris and Morrison hold, we show that if g is big enough, then F is a surface of positive index.

A note on Harris Morrison sweeping families

BEORCHIA, Valentina;
2014-01-01

Abstract

Harris and Morrison construct semistable families of k-gonal curves of genus g such that for every k the corresponding modular curves give a sweeping family in the k-gonal locus of the moduli space. Their construction depends on the choice of a smooth curve X. We show that if the genus g(X) is sufficiently high with respect to g then the geographical slope is 8 asymptotically with respect to g(X). Moreover, if some conjectured estimates given by Harris and Morrison hold, we show that if g is big enough, then F is a surface of positive index.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2816324
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