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On Chow and Picard groups of Richardson varieties
Abstract
We show that if Π⊆ G/P is a projected Richardson variety, then the degree map Pic(Π) → A1(Π)∨ is injective. Moreover, it is an isomorphism in characteristic zero and in all but finitely many positive characteristics. We conjecture that it is an isomorphism in every characteristic. Our proofs are geometric, using a linear paving, topological properties of klt singularities, and reduction to characteristic zero.
Related
BibTeX
@misc{anderson2026chow,
title = {{On Chow and Picard groups of Richardson varieties}},
author = {David Anderson and Sam Payne},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15161},
eprint = {2610.15161},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15161},
}
RIS
TY - UNPB
TI - On Chow and Picard groups of Richardson varieties
AU - David Anderson
AU - Sam Payne
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15161
UR - https://arxiv.org/abs/2610.15161
AB - We show that if Π⊆ G/P is a projected Richardson variety, then the degree map Pic(Π) → A_1(Π)^∨ is injective. Moreover, it is an isomorphism in characteristic zero and in all but finitely many positive characteristics. We conjecture that it is an isomorphism in every characteristic. Our proofs are geometric, using a linear paving, topological properties of klt singularities, and reduction to characteristic zero.
ER -