Using algebraic local cohomology with parameters
Katsusuke Nabeshima, Yayoi Nakamura, Shinichi Tajima
Last modified: 2010-05-28
Abstract
Recently, we showed that the use of algebraic local cohomology provides an efficient method for computing standard bases. We generalize this method to the case of parametric ideals for computing parametric standard bases and analyzing properties of singularities. In the algorithm generalized, we need a lot of techniques for treating equations with parameters. Some of the techniques are from comprehensive Groebner bases. In this presentation, we give the rough procedure for computing parametric algebraic local cohomology classes and their applications.