Seminar in Real & Complex Geometry

Thursday, 06.12.2012, 16:15-17:30, Schreiber building, room 210

Pinaki Mondal, Weizmann Institute

An effective criterion for algebraic contraction of curves


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.