Very special divisors on 4-gonal real algebraic curves

TL;DR

This paper investigates very special linear systems on 4-gonal real algebraic curves, classifying all such systems when the gonality is small, revealing new insights into their geometric properties.

Contribution

It provides a complete classification of very special linear systems on 4-gonal real algebraic curves with small gonality, expanding understanding of their structure.

Findings

Classification of very special linear systems for small gonality

Identification of conditions where Clifford inequality fails

Enhanced understanding of real algebraic curve geometry

Abstract

Given a real curve, we study special linear systems called "very special" for which the dimension does not satisfy a Clifford type inequality. We classify all these very special linear systems when the gonality of the curve is small.