Algebraic Geometry Seminar
Anton Leykin
University of Minnesota
Numerical primary decomposition
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.
Monday October 15, 2007 at 3:00 PM in SEO 712