Hyperelliptic Gorenstein curves and logarithmic differentials

Author:

Luca Battistella, Sebastian Bozlee

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Geometric Topology (math.GT)

journal:

date:

2023-07-07 16:00:00

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.

PDF: Hyperelliptic Gorenstein curves and logarithmic differentials.pdf