4 papers
Noncommutative resolutions of affine Schubert varieties in type A and canonical bases
Ilya Dumanski, Vasily Krylov
Given a resolution of an affine Schubert variety for , we define its noncommutative version --…
K-theoretic Hikita conjecture for quiver gauge theories
Ilya Dumanski, Vasily Krylov
We study variants of Hikita conjecture for Nakajima quiver varieties and corresponding Coulomb branches. First, we derive the equivariant version of the conjecture from the non-equ…
Perverse coherent sheaves on symplectic singularities
Ilya Dumanski
We propose the notion of perverse coherent sheaves for symplectic singularities and study its properties. In particular, it gives a basis of simple objects in the Grothendieck grou…
On reduced arc spaces of toric varieties
Ilya Dumanski, Evgeny Feigin, Ievgen Makedonskyi +1
An arc space of an affine cone over a projective toric variety is known to be non-reduced in general. It was demonstrated recently that the reduced scheme structure is worth studyi…