Negative Deformations of Toric Singularities that are Smooth in Codimension Two

  • Klaus Altmann
  • Lars Kastner
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 23)


Given a cone σ ⊆ N with smooth two-dimensional faces and, moreover, an element R ∈ σM of the dual lattice, we describe the part of the versal deformation of the associated toric variety TV(σ) that is built from the deformation parameters of multidegree R.

The base space is (the germ of) an affine scheme M̅ that reflects certain possibilities of splitting Q := σ [R = 1] into Minkowski summands.


Base Space Toric Variety Polyhedral Cone Versal Deformation Hilbert Basis 
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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2013

Authors and Affiliations

  • Klaus Altmann
    • 1
  • Lars Kastner
    • 1
  1. 1.Fachbereich Mathematik und Informatik, Institut für MathematikFreie Universität BerlinBerlinGermany

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