VersalDeformations : Table of Contents

• VersalDeformations -- calculating versal deformations and local Hilbert schemes
• CacheName -- determines hash table in which to cache solutions to the deformation equation
• checkComparisonTheorem -- checks if the Piene-Schlessinger or Di Dennaro comparison theorem holds
• checkTangentSpace -- checks if dimension of space of sections of the normal bundle agrees with that calculated using normalMatrix
• correctDeformation -- correct lifting to avoid obstructions at next order
• CorrectionMatrix -- determines the first order deformations used in correcting liftings
• correctionMatrix -- calculate how first order deformations perturb obstruction vector
• cotangentCohomology1 -- calculate first cotangent cohomology
• cotangentCohomology2 -- calculate second cotangent cohomology
• CT -- cotangent cohomology
• DefParam -- deformation parameter
• DegreeBound -- determines the degree limit used to compute the tangent cone of obstruction equations
• extMatrix -- calculate obstruction space for modules
• families -- outputs the perturbed families of a NestedDeformation
• firstOrderDeformations -- use tangent space to create first order perturbations and find relations
• HighestOrder -- sets the order to which we compute
• isPolynomial -- checks if a deformation lifts to arbitrary order
• liftDeformation -- lift a solution of the deformation equation to the next order
• liftDeformation(List,List,List,List) -- lift a solution of the deformation equation to the next order
• liftDeformation(NestedDeformation) -- lift a nested deformation to the next order
• localHilbertScheme -- computes a power series representation of the local Hilbert scheme
• NestedDeformation -- The class of all nested deformations
• nestedHilbertScheme -- computes a nested Hilbert scheme of a pair
• nestedObstruction -- calculate secondary obstruction space for nested deformations
• nestedTangent -- calculate first order deformations for nested deformations
• nestedVersalDeformation -- computes a nested VersalDeformation of a pair
• normalMatrix -- calculate normal module
• obstructions -- outputs the obstruction equations of a NestedDeformation
• PolynomialCheck -- checks if power series solution terminates
• SanityCheck -- checks if lifting solves deformation equation
• sanityCheck -- checks if deformation data satisfies the deformation equation at a certain order
• setupNestedDeformation -- create a first order NestedDeformation from tangent directions and obstruction spaces
• SmartLift -- chooses lifting to avoid obstructions at next order
• Verbose -- control the verbosity of output
• versalDeformation -- computes a power series representation of a versal deformation
• versalDeformation(List,List,List,List) -- continues calculation of a versal deformation
• versalDeformation(Matrix) -- computes a power series representation of a versal deformation
• versalDeformation(Matrix,Matrix,Matrix) -- computes a power series representation of a versal deformation
• versalDeformation(NestedDeformation) -- continues calculation of a versal deformation
• VersalDeformationResults -- hash table key for cached solutions to the deformation equation