Degeneracy Schemes and Schubert Varieties

Abstract

A result of Zelevinsky states that an orbit closure in the space of representations of the equioriented quiver of type $A_h$ is in bijection with the opposite cell in a Schubert variety of a partial flag variety $SL(n)/Q$. We prove that Zelevinsky's bijection is a scheme-theoretic isomorphism, which shows that the universal degeneracy schemes of Fulton are reduced and Cohen-Macaulay in arbitrary characteristic.

16 pp, Northeastern University, Latex

References in corpus (1)

• Universal Schubert polynomials

Cited by in corpus (4)

• Chern class formulas for quiver varieties
• Global F-regularity of Schubert varieties with applications to D-modules
• Universal Schubert polynomials
• Stanley symmetric functions and quiver varieties