Dual Infinite Wedge is $\mathrm{GL}_{\infty}$-equivariantly noetherian

TL;DR

This paper proves that a broad class of algebraic varieties, including the dual infinite wedge, are noetherian under the action of the infinite general linear group, extending previous results and providing constructive proofs.

Contribution

It establishes the equivariant noetherian property for a wide class of varieties, generalizing Plucker varieties and including the hyper-Pfaffians, with constructive proofs.

Findings

Proves equivariant noetherianity for dual infinite wedge

Extends previous results on bounded Plucker varieties

Provides constructive proof for hyper-Pfaffians

Abstract

We prove the (equivariant) noetherian property for a wide class of varieties generalizing the class of Plucker varieties (Theorem 1). It improves previous results of Draisma-Eggermont who treated the case of bounded Plucker varieties. Key ingredient of our proof is the constructive proof of the equivariant noetherianity for the hyper-Pfaffians (Theorem 36) which implies the equivariant noetherianity of the dual infinite wedge.