Singular del Pezzo surfaces and isotropic flag varieties

TL;DR

This paper computes the Chow quotient of a complete flag variety of isotropic subspaces in a four-dimensional complex vector space, revealing it to be a singular del Pezzo surface of degree four.

Contribution

It provides an explicit computation of the Chow quotient for isotropic flag varieties, connecting it to singular del Pezzo surfaces of degree four.

Findings

Chow quotient is a singular del Pezzo surface of degree four.

Explicit description of the Chow quotient for isotropic flag varieties.

New link between flag varieties and del Pezzo surfaces.

Abstract

We compute the Chow quotient of the complete flag variety of isotropic subspaces of a four dimensional complex vector space with respect to a skew/symmetric form, and show that it is a singular del Pezzo surface of degree four.