Back to Algebraic Geometry Seminar: Fall 2013
Algebraic Geometry Seminar
Date: Tuesday, Sep 17, 2013
Time: 3:30PM - 4:30PM
Location: LCB 225
Pinaki Mondal
University of Toronto
Title |
A new (and effective) criterion for contraction of rational curves on rational surfaces |
Abstract |
Let X be a non-singular rational algebraic surface (over C) equipped with a birational morphism to CP^2. Let L be a line on CP^2, and E’ be the union of the strict transform of L with all but one irreducible component of the exceptional divisor. Assume that the matrix of intersection numbers of components of E’ is negative definite, so that E' can be contracted to a normal analytic surface X’. Question: When is X' algebraic? I will present an answer in a geometric and then an algebraic form, and sketch the idea of the proof. The geometric answer in particular gives a correspondence between normal algebraic compactifications of C^2 with one (irreducible) curve at infinity and curves in C^2 with one (irreducible) branch at infinity. The reference for this talk is arXiv:1301.0126. If time permits, I will talk about a somewhat unexpected application in real algebraic geometry. |
Algebraic Geometry