New Techniques in Resolution of Singularities

D Abramovich, Michael Temkin, Jarosław Włodarczyk, Anne ühbis-Krüger

Research output: Book/ReportBookpeer-review

Abstract

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.
Original languageEnglish
Place of PublicationCham
Number of pages345
Edition1st ed. 2023
ISBN (Electronic)3031321154
DOIs
StatePublished - 2023

Publication series

NameOberwolfach Seminars
PublisherSpringer International Publishing; Imprint: Birkhäuser
Volume50

ULI publications

  • uli
  • Algebraic geometry
  • Geometry, Algebraic

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