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The dualizing sheaf on first-order deformations of toric surface singularities

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 Added by Klaus Altmann
 Publication date 2016
  fields
and research's language is English




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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



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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 parameters of multidegree R. Let Q the polyhedron obtained by intersecting sigma with the hyperplane R=1. Then the base space is (the germ of) an affine scheme that reflects certain possibilities of splitting Q into Minkowski summands.
210 - F.Malikov 2000
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.
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