deformMCMModule(...,DegreeLimit=>...) -- Compute only up to this exponent
Description
This parameter is an integer $ n $ such that in the result of the computation the versality criterion holds only after reducing the relevant rings modulo the maximal homogeneous ideal to the power $ n+1 $. Concretely, this means that the output may have incorrect terms with total exponent greater than $ n $. If the input is positively graded, all deformation parameters have strictly positive degree, and $ n $ is sufficiently large, then no terms of degree greater than $ n $ appear in the output, and the result is versal. In this case, the maximum of $ d / deg x $ where $ d $ is the degree of the equation of the hypersurface and $ x $ ranges over all variables in the ring of the hypersurface and all deformation parameters, should suffice.
Functions with optional argument named DegreeLimit:
- compose(Module,Module,Module,DegreeLimit=>...) -- see compose -- composition as a pairing on Hom-modules
- deformMCMModule(...,DegreeLimit=>...) -- Compute only up to this exponent
- End(...,DegreeLimit=>...) -- see End -- module of endomorphisms
- gb(...,DegreeLimit=>...) -- see gb -- compute a Gröbner basis
- Hom(...,DegreeLimit=>...) -- see Hom -- module of homomorphisms
- homomorphism'(...,DegreeLimit=>...) -- see homomorphism' -- get the element of Hom from a homomorphism
- minimalBetti(...,DegreeLimit=>...) -- see minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
- pushForward(...,DegreeLimit=>...) -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
- quotient(...,DegreeLimit=>...) (missing documentation)
- saturate(...,DegreeLimit=>...) (missing documentation)
- syz(...,DegreeLimit=>...) -- see syz(Matrix) -- compute the syzygy matrix
Further information
- Default value: 10
- Function: deformMCMModule -- versal deformation of MCM-module on hypersurface
- Option key: DegreeLimit -- an optional argument
The source of this document is in ModuleDeformations.m2:530:0.