PreprintCC BY-SA 4.0arXiv
Maximal geometric quotients of flag varieties
Abstract
We introduce the notion of maximal geometric quotient, namely a geometric quotient of a polarized pair under a torus action which has a birational contraction to any other GIT quotient. For the action of the maximal torus on a complete flag variety, we show that a maximal geometric quotient exists and it is a Mori dream space, and its Cox ring is isomorphic to the Cox ring of the flag variety. We discuss birational properties of the maximal geometric quotients, their relations with the Chow quotients and explain how to construct them for maximal torus actions on flag varieties.
Related
- Free-Monodromic Mixed Tilting Sheaves on Flag Varieties
- Independence of the Grothendieck classes of twisted symplectic flag varieties
- Minuscule Relations in Quantum K-Theory of Flag Varieties
- Semiorthogonal decompositions for families of twisted flag varieties
- Double flag varieties of Levi type with a finite number of orbits
BibTeX
@misc{barban2026maximal,
title = {{Maximal geometric quotients of flag varieties}},
author = {Lorenzo Barban and Michele Bianco and Luis E. Solá Conde},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37163},
eprint = {2610.37163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37163},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Maximal geometric quotients of flag varieties
AU - Lorenzo Barban
AU - Michele Bianco
AU - Luis E. Solá Conde
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37163
UR - https://arxiv.org/abs/2610.37163
AB - We introduce the notion of maximal geometric quotient, namely a geometric quotient of a polarized pair under a torus action which has a birational contraction to any other GIT quotient. For the action of the maximal torus on a complete flag variety, we show that a maximal geometric quotient exists and it is a Mori dream space, and its Cox ring is isomorphic to the Cox ring of the flag variety. We discuss birational properties of the maximal geometric quotients, their relations with the Chow quotients and explain how to construct them for maximal torus actions on flag varieties.
ER -