Automorphisms in Birational and Affine Geometry

Levico Terme, Italy, October 2012

  • Ivan Cheltsov
  • Ciro Ciliberto
  • Hubert Flenner
  • James McKernan
  • Yuri G. Prokhorov
  • Mikhail Zaidenberg
Conference proceedings

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 79)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Birational Automorphisms

    1. Front Matter
      Pages 1-1
    2. Ivan Arzhantsev, Andrey Popovskiy
      Pages 17-33
    3. Jérémy Blanc, Frédéric Mangolte
      Pages 35-58
    4. Ivan Cheltsov
      Pages 83-101
    5. Tommaso de Fernex
      Pages 103-120
    6. Thomas Eckl, Aleksandr Pukhlikov
      Pages 121-139
    7. Alex Massarenti, Massimiliano Mella
      Pages 149-167
  3. Automorphisms of Affine Varieties

    1. Front Matter
      Pages 239-239
    2. Abdallah Assi
      Pages 241-247
    3. Alexei Belov, Leonid Bokut, Louis Rowen, Jie-Tai Yu
      Pages 249-285
    4. Adrien Dubouloz, Lucy Moser-Jauslin, Pierre-Marie Poloni
      Pages 301-312
    5. Rajendra V. Gurjar, Kayo Masuda, Masayoshi Miyanishi
      Pages 327-361
    6. Drew Lewis
      Pages 407-430
    7. Vladimir Lin, Mikhail Zaidenberg
      Pages 431-467
    8. Leonid Makar-Limanov
      Pages 469-476
    9. Stefan Maubach, Roel Willems
      Pages 477-493
    10. Peter Russell
      Pages 495-518

About these proceedings


The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics.

Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference highlighted the close connections between the above-mentioned areas and promoted the exchange of knowledge and methods from adjacent fields.


14L30, 14E07, 14R20, 14R10, 32M17 Cremona group affine geometry automorphism group dynamics of automorphisms projective geometry

Editors and affiliations

  • Ivan Cheltsov
    • 1
  • Ciro Ciliberto
    • 2
  • Hubert Flenner
    • 3
  • James McKernan
    • 4
  • Yuri G. Prokhorov
    • 5
  • Mikhail Zaidenberg
    • 6
  1. 1.School of MathematicsUniversity of EdinburghEdinburghUnited Kingdom
  2. 2.Department of MathematicsUniversity of Rome Tor VergataRomeItaly
  3. 3.Faculty of MathematicsRuhr University BochumBochumGermany
  4. 4.Department of MathematicsUniversity of California San DiegoLa JollaUSA
  5. 5.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  6. 6.Institute Fourier, UMR 5582, CNRS-UJFUniversity of Grenoble ISaint Martin D’HèresFrance

Bibliographic information

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