CacheName is the name of an optional argument, whose value is either a mutable hash table or null. After each stage of lifting, the methods versalDeformation and localHilbertScheme will store the solution to the deformation equation in CacheName#VersalDeformationResults. If the value of CacheName is null as is the default, then the solution is stored in the hash table described in the documentation of versalDeformation and localHilbertScheme.