Linear degenerate symplectic flag varieties: symmetric degenerations and PBW locus

TL;DR

This paper studies linear degenerate symplectic flag varieties as symmetric degenerations, proving equivalences of degeneration orders and exploring geometric properties of the PBW locus from multiple perspectives.

Contribution

It introduces a new perspective on symplectic flag varieties as symmetric degenerations and establishes the equivalence of various degeneration orders.

Findings

Proved the equivalence of different degeneration orders.

Analyzed geometric properties of the PBW locus.

Realized degenerate varieties from multiple perspectives.

Abstract

We conceptualize in the paper the linear degenerate symplectic flag varieties as symmetric degenerations within the framework of type $A$ equioriented quivers. First, in the larger context of symmetric degenerations, we give a self-contained proof of the equivalence of different degeneration orders. Furthermore, we investigate the PBW locus: geometric properties of the degenerate varieties in this locus are proved by realizing them from different perspectives.