The rationality of the moduli space of two-pointed ineffective spin hyperelliptic curves

TL;DR

This paper proves that the moduli space of genus g ineffective spin hyperelliptic curves with two marked points is rational for all g ≥ 2, using geometric methods involving 3-fold quadrics.

Contribution

It establishes the rationality of the moduli space for these curves, a significant result in algebraic geometry, through geometric analysis of 3-fold quadrics.

Findings

The moduli space is rational for all g ≥ 2.

The geometric approach involves the use of 3-fold quadrics.

The result applies to genus g ineffective spin hyperelliptic curves with two marked points.

Abstract

By the geometry of the 3-fold quadric we show that the coarse moduli space of genus g ineffective spin hyperelliptic curves with two marked points is a rational variety for every $g \geq 2$.