New Techniques in Resolution of Singularities

1st ed. 2023

by Anne Fruhbis-Kruger , Dan Abramovich , Jaroslaw Wlodarczyk , Michael Temkin

Book Details

Format Paperback / Softback

Book Series Oberwolfach Seminars

ISBN-10 3031321146

ISBN-13 9783031321146

Edition 1st ed. 2023

Publisher Birkhauser Verlag AG

Imprint Birkhauser Verlag AG

Country of Manufacture GB

Country of Publication GB

Publication Date Sep 15th, 2023

Print length 326 Pages

Product Classification: Algebraic geometry

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Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced. The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.

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