VersalDeformations -- calculating versal deformations and local Hilbert schemes

Description

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, as well as deformations of modules.

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

• [DG89] Vincenzo Di Gennaro, A note on deformations of coherent sheaves, Boll. Un. Mat. Ital. B (7) 3 1989.
• [Si01] Arvid Siqveland, The Method of Computing Formal Moduli, Journal of Algebra 241, 2001.
• [St94] 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.
• [Si01] Arvid Siqveland, The Method of Computing Formal Moduli, Journal of Algebra 241, 2001.

The author thanks Jan Christophersen for helpful hints, especially regarding the computation of $T^2$.