100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Thierry Gallay

Karol Palka

On the log Minimal Model Program for surfaces with fractional boundary and its applications
星期一, 12 五月, 2014 - 10:30
Résumé : 

If we want to study a quasiprojective complex surface Y, it is natural to take its completion (X,D), where X is projective, X\D=Y and D is a reduced snc-divisor, the curve 'at infinity', and to study the log minimal model program run for the pair (X,D). However, the theorems of the program have to be supported by a detailed study of the effect on the open part X\D. This theory of 'open surfaces' has been developed by Miyanishi, Fujita and others for more than 40 years and turned out to be very successful. Now the program itself, although without an obvious geometric interpretation, works equally well when D is a Q-divisor. Recently we were able to adapt it to obtain progress in the classical
subject of classification of planar rational cuspidal curves.

Institution de l'orateur : 
Institut de Mathématiques, Varsovie
Thème de recherche : 
Algèbre et géométries
Salle : 
logo uga logo cnrs