A characterization of bielliptic curves via syzygy schemes

TL;DR

This paper characterizes bielliptic curves of genus at least 11 by examining their second syzygy schemes, providing a new criterion for identifying such curves based on algebraic properties.

Contribution

It establishes a novel characterization of bielliptic curves through the difference between the curve and its second syzygy scheme.

Findings

A canonical curve of genus ≥ 11 is bielliptic iff its second syzygy scheme differs from the curve.

Provides a new algebraic criterion for bielliptic curves based on syzygy schemes.

Enhances understanding of the relationship between syzygies and curve properties.

Abstract

We prove that a canonical curve $C$ of genus $\ge 11$ is bielliptic if and only if its second syzygy scheme $\mathrm{Syz}_2(C)$ is different from $C$.