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We explicitly describe infintesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Kollar-Shepherd-Barron and Viehweg. The conclusion is that in many cases these three notions are different from each other. In particular, we see that while the KSB and the Viehw
Given a polyhedral cone sigma with smooth two-dimensional faces and, moreover, a lattice point R in the dual cone of sigma, we describe the part of the versal deformation of the associated toric variety TV(sigma) that is built from the deformation pa
We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows us to compute the cohomology of the chiral de Rham complex over the projective space.
It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an affine space can be overall resolved by means of projective torus-equivariant crepant birational morphi
In previous work, the authors have developed a geometric theory of fundamental strata to study connections on the projective line with irregular singularities of parahoric formal type. In this paper, the moduli space of connections that contain regul
Let the vector bundle $mathcal{E}$ be a deformation of the tangent bundle over the Grassmannian $G(k,n)$. We compute the ring structure of sheaf cohomology valued in exterior powers of $mathcal{E}$, also known as the polymology. This is the first par