Deformations of Toric Varieties via Minkowski Sum Decompositions of Polyhedral Complexes
arXiv:0902.0967
Abstract
We generalized the construction of deformations of affine toric varieties of K. Altmann and our previous construction of deformations of weak Fano toric varieties to the case of arbitrary toric varieties by introducing the notion of Minkowski sum decompositions of polyhedral complexes. Our construction embeds the original toric variety into a higher dimensional toric variety where the image is given by a prime binomial complete intersection ideal in Cox homogeneous coordinates. The deformations are realized by families of complete intersections. For compact simplicial toric varieties with at worst Gorenstein terminal singularities, we show that our deformations span the infinitesimal space of deformations by Kodaira-Spencer map. For Fano toric varieties, we show that their deformations can be constructed in higher-dimensional Fano toric varieties related to the Batyrev-Borisov mirror symmetry construction.
References in corpus (2)
Cited by in corpus (14)
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- Mutations of Laurent Polynomials and Flat Families with Toric Fibers
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- Mirror Symmetry and smoothing Gorenstein toric affine 3-folds
- Families of Invariant Divisors on Rational Complexity-One T-Varieties
- Degenerations and mirror contractions of Calabi-Yau complete intersections via Batyrev-Borisov Mirror symmetry
- Toric Degenerations and the Laurent polynomials related to Givental's Landau-Ginzburg models
- On deformation spaces of toric singularities and on singularities of K-moduli of Fano varieties
- Deformations of Smooth Complete Toric Varieties: Obstructions and the Cup Product
- Mirror Symmetry for Calabi-Yau complete intersections in Fano toric varieties
- On deformations of toric varieties