Mathematical Research Letters

Volume 30 (2023)

Number 2

Mather classes of Schubert varieties via small resolutions

Pages: 463 – 507



Minyoung Jeon (Department of Mathematics, Ohio State University, Columbus, Oh., U.S.A.; and Department of mathematics, University of Georgia, Athens, Ga., U.S.A.)


We express Schubert expansions of the Chern–Mather classes for Schubert varieties in the even orthogonal Grassmannians via integrals involving Pfaffians and pushforward of the small resolutions in the sense of Intersection Cohomology (IH) constructed by Sankaran and Vanchinathan, instead of the Nash blowup. The equivariant localization is employed to show the way of computing the integrals. As byproducts, we present the computations. For analogy and the completion of the method in ordinary Grassmannians, we also suggest Kazhdan–Lusztig classes associated to Schubert varieties in the Lagrangian and odd orthogonal Grassmannians.

Received 11 December 2021

Received revised 25 June 2023

Accepted 21 July 2023

Published 13 September 2023