Mathematics – Algebraic Geometry
Scientific paper
1994-03-02
Mathematics
Algebraic Geometry
17 pages, LaTeX, Preprint 9/93 Humboldt-Universitaet Berlin
Scientific paper
For an affine, toric 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 dim Y=3 (dim Q=2). For this particular case, so-called toric deformations of Y correspond to Minkowski decompositions of Q into a sum of lattice polygons. Their Kodaira-Spencer-map can be interpreted in a very natural way. We regard the projective variety P(Y) defined by the lattice polygon Q. Data concerning the deformation theory of Y can be interpreted as data concerning the Picard group of P(Y). Finally, we provide some examples (the cones over the toric Del Pezzo surrfaces). There is one such variety yielding Spec C[e]/e^2 as the base space of the semi-universal deformation.
No associations
LandOfFree
Toric Q-Gorenstein Singularities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Toric Q-Gorenstein Singularities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Toric Q-Gorenstein Singularities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-63569