Anton Leykin : Numerical primary decomposition

Posted by , part of the Algebraic Geometry Seminar.

At

Oct. 15, 2007, 3 p.m.

In

SEO 712

Abstract

The existing methods for numerical algebraic geometry give a way to decompose an affine complex variety $X$ into irreducible components. The collection of numerical presentations for these components corresponds to minimal primes associated to the defining ideal $I=I(X)$ of the variety. We propose a method to find embedded components of $I$. Moreover, we give a numerical description of the scheme Spec$(I)$ by means of {\em numerical primary decomposition}. This description, in particular, solves the ideal membership problem for the ideal $I$. The main ingredient is the construction of a {\em deflated variety} in a higher-dimensional ambient space, which is related to higher Nash blowups.