The Prym-canonical Clifford index

TL;DR

This paper introduces new invariants for Prym curves, classifies them based on these invariants, and computes their values for general Prym curves, advancing understanding of Prym-canonical properties.

Contribution

It defines the Prym-canonical Clifford index and dimension, classifies Prym curves by these invariants, and computes their values for general Prym curves.

Findings

Classified Prym curves with Clifford index 0, 1, 2.

Computed Prym-canonical Clifford index for general Prym curves.

Established that the Prym-canonical Clifford dimension of a general Prym curve is (0,0).

Abstract

We introduce two new invariants of Prym curves, the Prym-canonical Clifford index and the Prym-canonical Clifford dimension. The former is a nonnegative integer (according to Prym-Clifford's theorem), while the latter is a pair of nonnegative ordered integers. We classify Prym curves with Prym-canonical Clifford index equal to 0,1,2. By specialization to hyperelliptic curves, we compute the Prym-canonical Clifford index of a general Prym curve and show that its Prym-canonical Clifford dimension is (0,0).