Some Applications of Duality Between
Polynomials and Formal Series
Date: July 19th (Friday)
Time: 14:00-14:25
Abstract
We are going to describe a duality between the algebra of
polynomials and the algebra of formal series, viewed as a space of
differential operators. This duality is connected to the notion of inverse
systems introduced by Macaulay (1916). We will recall the main properties
of these inverse systems and see how difficult operation on ideals become
easier with formalism. Then we will focus on 0-dimensional ideals
and show how the local ring of an isolated point can
be computed by integration in the dual space.
We will give some applications to the computation of local residues
in the case of complete intersection, to the analysis of real branches of
locally complete intersection case. We will end by some computations of
global residues, where formal series appear explicitly. Some connections
with Grobner bases computations will also be illustrated.
