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arXiv · 1808.01290

The strong maximal rank conjecture and moduli spaces of curves

Fu Liu·Brian Osserman·Montserrat Teixidor i Bigas·Naizhen Zhang
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Abstract

Building on recent work of the authors, we use degenerations to chains of elliptic curves to prove two cases of the Aprodu-Farkas strong maximal rank conjecture, in genus $22$ and $23$. This constitutes a major step forward in Farkas' program to prove that the moduli spaces of curves of genus $22$ and $23$ are of general type. Our techniques involve a combination of the Eisenbud-Harris theory of limit linear series, and the notion of linked linear series developed by the second author.

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Fu Liu, Brian Osserman, Montserrat Teixidor i Bigas, Naizhen Zhang. 2018-12-07. The strong maximal rank conjecture and moduli spaces of curves. https://doi.org/10.2140/ant.2024.18.1403

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