The resolution of singular algebraic varieties : Clay Mathematics Institute Summer School 2012: The Resolution of Singular Algebraic Varieties, Obergurgl, Tyrolean Alps, Austria, June 3-30, 2012

Description

Resolution of Singularities has long been considered as being a difficult to access area of mathematics. The more systematic and simpler proofs that have appeared in the last few years in zero characteristic now give us a much better understanding of singularities. They reveal the aesthetics of both the logical structure of the proof and the various methods used in it. The present volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution. As such, it provides a gentle and quite comprehensive introduction to this amazing field. The book may tempt the reader to enter more deeply into a topic where many mysteries--especially the positive characteristic case--await to be disclosed. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA) Content: * Blowups and resolution by H. Hauser* On the behavior of the multiplicity on schemes: Stratification and blow ups by A. Bravo and O. E. Villamayor U.* A simplified game for resolution of singularities by J. Schicho* Resolution of singularities in char p and monomialization by S. D. Cutkosky* Resolution of toric varieties by S. Encinas* Desingularization in computational applications and experiments by A. Fruhbis-Kruger* Introduction to the idealistic filtration program with emphasis on the radical saturation by H. Kawanoue* Algebraic approaches to FlipIt by J. Schicho and J. Top* Higher Semple-Nash blowups and F-blowups by T. Yasuda