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arXiv · 1211.2827

Sharp slope bounds for sweeping families of trigonal curves

Anand Deopurkar·Anand Patel
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Abstract

We establish sharp bounds for the slopes of curves in $\bar{M}_g$ that sweep the locus of trigonal curves, proving Stankova-Frenkel's conjectured bound of $7+6/g$ for even $g$ and obtaining the bound $7+20/(3g+1)$ for odd $g$. For even $g$, we find an explicit expression of the so-called Maroni divisor in the Picard group of the space of admissible triple covers. For odd $g$, we describe the analogous extremal effective divisor and give a similar explicit expression.

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Anand Deopurkar, Anand Patel. 2012-11-12. Sharp slope bounds for sweeping families of trigonal curves. https://arxiv.org/abs/1211.2827

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