Subcanonical points on algebraic curves

TL;DR

This paper investigates subcanonical points on algebraic curves, characterizing their gap sequences and constructing examples with specific ramification properties, advancing understanding of special points on algebraic curves.

Contribution

It computes gap sequences at general subcanonical points and constructs examples with various sequences via cyclic covers, providing new insights into their structure.

Findings

Computed gap sequences at general subcanonical points.

Constructed subcanonical points with specific ramification sequences.

Linked subcanonical points to cyclic cover constructions.

Abstract

A point of an algebraic curve of genus g is subcanonical if some regular differential vanishes only at that point, with multiplicity 2g-2. Subcanonical points are Weierstrass points, and we compute the associated gap sequence at a general point of each component of the moduli space of curves with marked subcanonical point. We also construct subcanonical points with other gap sequences as ramification points of certain cyclic covers.