Seminar in Real & Complex Geometry

Wednesday, 26.02.2014, 16:00-17:30, Schreiber building, room 209

Pinaki Mondal, Weizmann Institute

Towards a constructive theory of compactifications of $C^n$


The talk will be about a method for explicit construction of compactifications of $C^n$ with some desired properties at infinity. The main tool for the construction is a global variant of "key polynomial" of a valuation (key polynomial was introduced by MacLane and is a basic tool in valuation theory). The original motivation was applications to the "affine Bezout problem" of finding number of solutions in $C^n$ of a given system of polynomials; however, the explicitness of the construction makes it applicable to other problems, e.g. computation of cohomologies of line bundles, or determination of topology at infinity, and a big part of these problems boils down to combinatorics in almost the same spirit of (projective) toric varieties. In this talk I will focus on the dimension two case, where things are relatively more transparent. The general case will (hopefully) be the topic of a future talk.