Resolution of Singularities

A research textbook in tribute to Oscar Zariski Based on the courses given at the Working Week in Obergurgl, Austria, September 7-14, 1997
Erscheinungsjahr 2012
ISBN: 978-3-0348-9550-7
Verlag: Birkhäuser

Buch, Englisch, 598 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 931 g

Reihe: Progress in Mathematics

In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems.

Zielgruppe

Research

Autoren/Hrsg.

Hauser, Herwig

Lipman, Joseph

Oort, Frans

Quiros, Adolfo

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Oscar Zariski 1899–1986.- Resolution of Singularities 1860–1999.- 1: Classes of the Working Week.- Alterations and resolution of singularities.- Reduction of singularities for differential equations.- Puiseux solutions of singular differential equations.- A course on constructive desingularization and equivariance.- 2: Contributions.- A computer program for the resolution of singularities.- Uniformisation et désingularisation des surfaces d’après Zariski.- Tonie varieties and toric resolution.- A compactification of a fine moduli space of curves.- Applications of de Jong’s theorem on alterations.- Resolving singularities of plane analytic branches with one toric morphism.- Excellent surfaces and their taut resolution.- An application of alterations to Dieudonné modules.- Valuation theoretic and model theoretic aspects of local uniformization.- Les singularités Sandwich.- Equisingularity and simultaneous resolution of singularities.- Resolution of weighted homogeneous surface singularities.- Alterations and birational anabelian geometry.- The turbulent fifties in resolution of singularities.- Valuations.