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The strong maximal rank conjecture and moduli spaces of curves

Fu Liu, Brian Osserman, Montserrat Teixidor i Bigas and Naizhen Zhang

Vol. 18 (2024), No. 8, 1403–1464
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 Osserman.

Keywords
maximal rank, moduli space, algebraic curve, general type
Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 14H51, 14D06
Milestones
Received: 8 October 2019
Revised: 19 August 2022
Accepted: 11 September 2023
Published: 18 September 2024
Authors
Fu Liu
Department of Mathematics
University of California, Davis
Davis, CA
United States
Brian Osserman
Department of Mathematics
University of California, Davis
Davis, CA
United States
Montserrat Teixidor i Bigas
Department of Mathematics
Tufts University
Medford, MA
United States
Naizhen Zhang
Fairleigh Dickinson University
Vancouver Campus
Vancouver, BC
Canada

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