Work

Initial degenerations of flag varieties

Year: 2025

Type: article

Abstract: We prove that the initial degenerations of the flag variety admit closed immersions into finite inverse limits of flag matroid strata, where the diagrams are derived from matroidal subdivisions of a suitable flag matroid polytope. As an application, we prove that the initial degenerations of $\mathrm{F}\ell^{\circ}(n)$ –the open subvariety of the complete flag variety $\mathrm{F}\ell(n)$ consisting of flags in general position—are smooth and irreducible when $n\leq 4$ . We also study the Chow quotient of $\mathrm{F}\ell(n)$ by the diagonal torus of $\textrm{PGL}(n)$ and show that, for $n=4$ , this is a log crepant resolution of its log canonical model.

Source: Mathematical Proceedings of the Cambridge Philosophical Society

DOI: 10.1017/s0305004125101783

Authors: DANIEL COREY, JORGE ALBERTO OLARTE

Institutions: Embry-Riddle Aeronautical University Daytona Beach Florida Campus, Embry–Riddle Aeronautical University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: G1372115314, G2033548659, TRR 195: Symbolische Werkzeuge in der Mathematik und ihre Anwendung, G743358325, EXC 2046: MATH+: Berlin Mathematics Research Center