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VersalDeformations :: VersalDeformations

VersalDeformations -- calculating versal deformations and local Hilbert schemes


This package provides tools for calculating tangent and obstruction spaces as well as power series solutions for deformation problems involving isolated singularities and projective schemes.

A basic description of the package's approach to deformation problems can be found at the documentation node for versalDeformation. For details and mathematical background see

  • Jan Stevens, Computing Versal Deformations, Experimental Mathematics Vol. 4 No. 2, 1994.

The numerous examples presented in the documentation nodes for versalDeformation and localHilbertScheme are classical deformation problems, considered in the following articles:

  • [Al97] Klaus Altmann, The versal deformation of an isolated Gorenstein singularity, Inventiones Mathematicae Vol. 128 No. 3, 443-479 1997.
  • [CS10] Dustin Cartwright and Bernd Sturmfels, The Hilbert scheme of the diagonal in a product of projective spaces, International Mathematics Research Notices Vol. 2010 No. 9, 1741-1771.
  • [PS85] Ragni Piene and Michael Schlessinger, On the Hilbert scheme compactification of the space of twisted cubic curves, American Journal of Mathematics, Vol. 107 No. 4, 761-774, 1985.
  • [Pi74] Henry Pinkham, Deformations of algebraic varieties with G_m action, Asterisque 20, 1974.

The author thanks Jan Christophersen for helpful hints, especially regarding the computation of T2.


Certification a gold star

Version 1.0 of this package was accepted for publication in volume 4 of the journal The Journal of Software for Algebra and Geometry: Macaulay2 on 2012-06-05, in the article Versal deformations and local Hilbert schemes. That version can be obtained from the journal or from the Macaulay2 source code repository, svn://, release number 14710.


This documentation describes version 2.0 of VersalDeformations.

Source code

The source code from which this documentation is derived is in the file VersalDeformations.m2.