Hyperelliptic Gorenstein curves and logarithmic differentials

TL;DR

The paper introduces a new method for contracting subcurves in logarithmic hyperelliptic curves and demonstrates how hyperelliptic multiscale differentials relate to Gorenstein contractions, providing evidence for a broader conjecture about differential limits.

Contribution

It develops a local, base-change compatible contraction tool for logarithmic hyperelliptic curves and links multiscale differentials to Gorenstein contractions of nodal curves.

Findings

Hyperelliptic multiscale differentials induce Gorenstein contractions.

The contraction process is local and compatible with base change.

Provides evidence for a conjecture on limits of differentials.

Abstract

We produce a flexible tool for contracting subcurves of logarithmic hyperelliptic curves, which is local around the subcurve and commutes with arbitrary base-change. As an application, we prove that hyperelliptic multiscale differentials determine a sequence of Gorenstein contractions of the underlying nodal curve, whose dualising bundle they descend to generate. This is the first piece of evidence for a more general conjecture about limits of differentials.