A note on Harris Morrison sweeping families of maximal gonality
Abstract
Harris and Morrison constructed semistable families f:F \to Y 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 in 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 ratio K_F^2 / \chi(O_F) is 8 asymptotically with respect to g(X). We show also that if the gonality is maximal and some conjectured estimates of Harris and Morrison hold, the slope of the fibration f: F\to Y is 12 asymptotically with respect to g and that F is a surface of positive index.
Keywords
Cite
@article{arxiv.1302.0620,
title = {A note on Harris Morrison sweeping families of maximal gonality},
author = {Valentina Beorchia and Francesco Zucconi},
journal= {arXiv preprint arXiv:1302.0620},
year = {2013}
}
Comments
We added an hypothesis in the statement of Proposition 3.2, which holds if some conjectured estimates of Harris-Morrison are true