Coherent systems of genus 0, III: Computation of flips for k=1

TL;DR

This paper studies the variation of moduli spaces of coherent systems of type (n,d,1) on the projective line as the stability parameter varies, explicitly describing flips and computing Hodge polynomials for ranks 2 and 3.

Contribution

It provides an explicit description of flips and moduli space changes for k=1 coherent systems, including detailed calculations for ranks 2 and 3.

Findings

Determined the first and last moduli spaces and flip loci.

Explicitly described moduli space transformations for ranks 2 and 3.

Computed Hodge polynomials for ranks 2 and 3.

Abstract

In this paper we continue the investigation of coherent systems of type $(n,d,k)$ on the projective line which are stable with respect to some value of a parameter $\alpha$. We consider the case $k=1$ and study the variation of the moduli spaces with $\alpha$. We determine inductively the first and last moduli spaces and the flip loci, and give an explicit description for ranks 2 and 3. We also determine the Hodge polynomials explicitly for ranks 2 and 3 and in certain cases for arbitrary rank.