Structure constants for Chern classes of Schubert cells
Changjian Su
TL;DR
This paper extends known formulas for Schubert class multiplication to Chern--Schwartz--MacPherson and Segre--Schwartz--MacPherson classes of Schubert cells, providing new explicit structure constants in algebraic geometry.
Contribution
It derives explicit formulas for the structure constants of CSM and SSM classes of Schubert cells, generalizing previous results for Schubert classes.
Findings
Formulas for structure constants of CSM classes.
Formulas for structure constants of SSM classes.
Connection to stable basis elements in the cotangent bundle.
Abstract
A formula for the structure constants of the multiplication of Schubert classes is obtained in arXiv:1909.05283. In this note, we prove analogous formulae for the Chern--Schwartz--MacPherson (CSM) classes and Segre--Schwartz--MacPherson (SSM) classes of Schubert cells in the flag variety. By the equivalence between the CSM classes and the stable basis elements for the cotangent bundle of the flag variety, a formula for the structure constants for the latter is also deduced.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology