Toric I Q-gorenstein Singularities
نویسنده
چکیده
For an affine, toric I Q-Gorenstein variety Y (given by a lattice polytope Q) the vector space T 1 of infinitesimal deformations is related to the complexified vector spaces of rational Minkowski summands of faces of Q. Moreover, assuming Y to be an isolated, at least 3-dimensional singularity, Y will be rigid unless it is even Gorenstein and dimY = 3 (dimQ = 2). For this particular case, so-called toric deformations of Y correspond to Minkowski decompositions of Q into a sum of lattice polygons. Their KodairaSpencer-map can be interpreted in a very natural way. We regard the projective variety IP (Y ) defined by the lattice polygon Q. Data concerning the deformation theory of Y can be interpreted as data concerning the Picard group of IP (Y ). Finally, we provide some examples (the cones over the toric Del Pezzo surfaces). There is one such variety yielding Spec I C[ε]/ ε as the base space of the semi-universal deformation.
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