Singularities of closures of spherical $B$-conjugacy classes of nilpotent orbits

Abstract

We prove that for a simply laced group, the closure of the Borel conjugacy class of any nilpotent element of height $2$ in its conjugacy class is normal and admits a rational resolution. We extend this, using Frobenius splitting techniques, to the closure in the whole Lie algebra if either the group has type $A$ or the element has rank $2$.

23 pages. Replaces arXiv:1412.5654. New results added

References in corpus (2)

• Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries
• Normality of Orthogonal and Sympletic Nilpotent Orbit Closures in Positive Characteristic

Cited by in corpus (1)

• Loop Models and $K$-Theory