On rigidity of flag varieties
Andrzej Weber, Jaros{\l}aw A. Wi\'sniewski
TL;DR
This paper proves that the variety of complete flags for any semisimple algebraic group remains unchanged in any smooth family of Fano manifolds, demonstrating its rigidity in such geometric contexts.
Contribution
It establishes the rigidity of flag varieties within smooth families of Fano manifolds, extending understanding of their stability under deformations.
Findings
Flag varieties are rigid in smooth Fano families.
Rigidity holds for all semisimple algebraic groups.
Supports stability of geometric structures in algebraic geometry.
Abstract
We prove that the variety of complete flags for any semisimple algebraic group is rigid in any smooth family of Fano manifolds.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation