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TitleResolution of Singularities [electronic resource] : A research textbook in tribute to Oscar Zariski Based on the courses given at the Working Week in Obergurgl, Austria, September 7-14, 1997 / edited by Herwig Hauser, Joseph Lipman, Frans Oort, Adolfo Quirรณs
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2000
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8399-3
Descript XXI, 598 p. online resource

SUMMARY

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


CONTENT

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 dรฉsingularisation des surfaces dโ{128}{153}aprรจs Zariski -- Tonie varieties and toric resolution -- A compactification of a fine moduli space of curves -- Applications of de Jongโ{128}{153}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 Dieudonnรฉ modules -- Valuation theoretic and model theoretic aspects of local uniformization -- Les singularitรฉs 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


Mathematics Algebraic geometry Applied mathematics Engineering mathematics Topology Mathematics Algebraic Geometry Topology Applications of Mathematics



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