Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

New Techniques in Resolution of Singularities

  • Textbook
  • © 2023
Download book PDF
Download book EPUB

Overview

Authors:
  1. Dan Abramovich

    1. Department of Mathematics, Brown University, Providence, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Anne Frühbis-Krüger

    1. Institut für Mathematik, Universität Oldenburg, Oldenburg, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Michael Temkin

    1. Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel

    View author publications

    You can also search for this author in PubMed   Google Scholar

  4. Jarosław Włodarczyk

    1. Department of Mathematics, Purdue University West Lafayette, West Lafayette, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Gives an introduction to stacks
  • Includes an introduction to logarithmic geometry
  • Presents techniques of resolution of singularities

Part of the book series: Oberwolfach Seminars (OWS, volume 50)

Buy print copy

Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. A Computational View on Hironaka’s Resolution of Singularities

    • Anne Frühbis-Krüger
    Pages 1-61
    Download chapter PDF

  3. Stacks for Everyone Who Cares About Varieties and Singularities

    • Dan Abramovich
    Pages 63-86
    Download chapter PDF

  4. Introduction to Logarithmic Geometry

    • Michael Temkin
    Pages 87-122
    Download chapter PDF

  5. Birational Geometry Using Weighted Blowing Up

    • Dan Abramovich, Michael Temkin, Jarosław Włodarczyk
    Pages 123-138
    Download chapter PDF

  6. Relative and Logarithmic Resolution of Singularities

    • Michael Temkin
    Pages 139-218
    Download chapter PDF

  7. Weighted Resolution of Singularities. A Rees Algebra Approach

    • Jarosław Włodarczyk
    Pages 219-317
    Download chapter PDF

  8. New Techniques in Resolution of Singularities: Open Problems

    • Dan Abramovich, Anne Frühbis-Krüger, Michael Temkin, Jarosław Włodarczyk
    Pages 319-326
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Brown University, Providence, USA

    Dan Abramovich

  • Institut für Mathematik, Universität Oldenburg, Oldenburg, Germany

    Anne Frühbis-Krüger

  • Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel

    Michael Temkin

  • Department of Mathematics, Purdue University West Lafayette, West Lafayette, USA

    Jarosław Włodarczyk

About the authors

Dan Abramovich studied mathematics at Tel Aviv University and at Harvard, where he received his PhD in 1991. After a postdoctoral fellowship at MIT, he was on faculty at Boston University, where he was Sloan Research Fellow, before moving to Brown University where he is L. Herbert Ballou University Professor. He is Fellow of the American Mathematical Society and the American Association for the Advancement of Science. He works in birational Geometry, Moduli Spaces, and Arithmetic Geometry. His 2018 ICM talk at Rio de Janeiro focused on material described in the present book. 

Anne Frühbis-Krüger works in computational algebraic geometry and singularity theory. She received her PhD from Kaiserslautern University in 2000. After a visiting professorship at FU Berlin and more than a decade as apl. Professor at Leibniz Universität Hannover, she moved to her current position at Universität Oldenburg in 2019. She has served as the spokespersonof the 'Fachgruppe Computeralgebra' for two periods and is actively involved in the development of the computer algebra systems Singular and OSCAR.

Michael Temkin is the Maurice and Clara Weil Chair in Mathematics at the Hebrew University of Jerusalem. His main research interests lie within non-archimedean geometry, birational geometry and the interplay between them. In particular, he is interested in resolution of singularities and semistable reduction problems. He graduated from the Weizmann Institute of Science in 2006, and after a postdoc at the University of Pennsylvania and a one-year membership at the IAS joined the Hebrew University of Jerusalem in 2010. Since 2020 he is serving as the editor in chief of the Israel Journal of Mathematics.

Jarosław Włodarczyk works in birational geometry and resolution of singularities. He graduated from Warsaw University in 1993. After a visiting position in Ruhr University Bochum and a scholarship at Grenoble University, he joined Warsaw University where he worked till 2000. After that he moved to Purdue University, where he is now a professor at the Department of Mathematics. Jarosław Włodarczyk was an invited speaker in ICM Madrid 2006, where he presented his work on the weak Factorization Theorem, playing an important role in Algebraic Geometry. He is also a recipient of numerous awards for his research contributions to birational geometry.

Bibliographic Information

  • Book Title: New Techniques in Resolution of Singularities

  • Authors: Dan Abramovich, Anne Frühbis-Krüger, Michael Temkin, Jarosław Włodarczyk

  • Series Title: Oberwolfach Seminars

  • DOI: https://doi.org/10.1007/978-3-031-32115-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Softcover ISBN: 978-3-031-32114-6Published: 15 September 2023

  • eBook ISBN: 978-3-031-32115-3Published: 14 September 2023

  • Series ISSN: 1661-237X

  • Series E-ISSN: 2296-5041

  • Edition Number: 1

  • Number of Pages: XX, 326

  • Number of Illustrations: 3 b/w illustrations, 9 illustrations in colour

  • Topics: Algebraic Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation