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arXiv · 2005.01884

Versality in toric geometry

Klaus Altmann·Alexandru Constantinescu·Matej Filip
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Abstract

We study deformations of affine toric varieties. The entire deformation theory of these singularities is encoded by the so-called versal deformation. The main goal of our paper is to construct the homogeneous part of some degree -R of this, i.e. a maximal deformation with prescribed tangent space T^1(-R) for a given character R. To this aim we use the polyhedron obtained by cutting the rational cone defining the affine singularity with the hyperplane defined by [R=1]. Under some length assumptions on the edges of this polyhedron, we provide the versal deformation for primitive degrees R.

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Klaus Altmann, Alexandru Constantinescu, Matej Filip. 2020-05-04. Versality in toric geometry. https://arxiv.org/abs/2005.01884

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