Rationality of fields of invariants for some representations of SL(2)\timesSL(2)

TL;DR

This paper proves that the field of invariants for certain SL(2)×SL(2) representations, specifically the quotient of bidegree (a, b) curves on P^1×P^1, is rational under specific conditions.

Contribution

It establishes the rationality of the invariant field for the action of SL(2)×SL(2) on bidegree (a, b) curves when ab is even and a≠b, extending understanding of invariant fields.

Findings

The quotient space is rational when ab is even and a≠b.

The result applies to the space of bidegree (a, b) curves on P^1×P^1.

Provides new cases where invariant fields are proven to be rational.

Abstract

We prove that the quotient by SL(2)\timesSL(2) of the space of bidegree (a, b) curves on P^1\timesP^1 is rational when ab is even and a\not=b.