Unirationality of the Hurwitz space H_{9,8}

TL;DR

This paper proves the unirationality of the Hurwitz space H_{9,8}, demonstrating it is parametrized by rational functions, and provides an explicit computational method using Macaulay2 to construct relevant algebraic curves.

Contribution

The paper establishes the unirationality of H_{9,8} and offers an explicit computational approach for constructing the associated algebraic curves.

Findings

H_{9,8} is unirational.

Provides an explicit Macaulay2 code for curve construction.

Constructs a nodal curve of degree 8 and genus 9 with 12 double points.

Abstract

In this paper we prove that the Hurwitz space H_{9,8}, which parameterizes 8-sheeted covers of P^1 by curves of genus 9, is unirational. Our construction leads to an explicit Macaulay2 code, which will randomly produce a nodal curve of degree 8 of geometric genus 9 with 12 double points and together with a pencil of degree 8.