Standard Monomial Theory of RR varieties
Philip Foth, Sangjib Kim
TL;DR
This paper develops a standard monomial theory for RR varieties, constructed as fiber products of Bott-Samelson and Richardson varieties, and analyzes their coordinate rings.
Contribution
It introduces a new standard monomial framework for RR varieties and explores their algebraic structure.
Findings
Established a basis for coordinate rings of RR varieties.
Connected RR varieties to existing geometric structures.
Provided tools for further algebraic and geometric analysis.
Abstract
We construct the RR varieties as the fiber products of Bott-Samelson varieties over Richardson varieties. We study their homogeneous coordinate rings and standard monomial theory.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory