Susanna Zimmermann ☰

About Me

Me

Professor
Departement Mathematik und Informatik, Universität Basel
(detachement at Institut de mathématiques d'Orsay, University of Paris-Saclay)

Contacts: susanna.zimmermann@Sunibas.ch (take away the obvious letter)
susanna.zimmermann@Suniversite-paris-saclay.fr (take away the obvious letter)

Research interests: birational geometry, Cremona groups, algebraic groups, real algebraic geometry
ORCID iD iconhttps://orcid.org/0000-0002-2216-7712

CV: english, français

Publications

Preprints

Published articles

  1. Birational involutions of the real projective plane (with Ivan Cheltsov, Frédéric Mangolte and Egor Yasinsky) [pdf] (07/2022), to appear in JEMS
  2. Properties of the Cremona group endowed with the Euclidean topology (with Hannah Bergner) [pdf] Bull. of the Lond. Math. Soc., vol. 55 (2023), issue 4, 1817-1836.
  3. Factorization centers in dimension two and the Grothendieck ring of varieties (with Hsueh-Yung Lin and Evgeny Shinder), to appear in Algebraic Geometry [pdf]
  4. Small G-varieties (with Hanspeter Kraft and Andriy Regeta) to appear in Canadian J. of Math., 2024; 76(1), 173-215. [pdf][official page]
  5. A remark on Geiser involutions, Special New Zealand volume, Europ. J. of Math, 2022 [pdf] [official link]
  6. Bijective Cremona transformations of the plane (with Shamil Asgarli, Kuan-Wen Lai and Masahiro Nakahara), Selecta Math. New Ser. 28, 53 (2022)[pdf]
  7. Algebraic subgroups of the plane Cremona group over a perfect field (with Julia Schneider)
    EpiGA, vol. 5 (2021), no. 14 [pdf]
  8. Continuous automorphisms of Cremona groups (with Christian Urech)
    Int. J. of Math., vol. 32, no.4 (2021) [pdf]
  9. Quotients of higher dimensional Cremona groups (with J. Blanc and S. Lamy)
    Acta Math. Vol. 226, No. 2 (2021), pp. 211-318 [pdf]
  10. The real plane Cremona group is a non-trivial amalgam
    Annales de l'Institut Fourier, Volume 71 (2021) no. 3, pp. 1023-1045 [pdf]
  11. Signature morphisms from the Cremona group over a non-closed field (with S. Lamy)
    J. Eur. Math. Soc. 22 (2020), 3133-3173 [pdf]
  12. A new presentation of the plane Cremona group (with C. Urech)
    Proceedings of the AMS, vol. 147, no. 7 (2019) 2741-2755. [pdf]
  13. The decomposition groups of plane conics and plane rational cubics (with T. Ducat and I. Heden)
    Math. Res. Lett., 26(1) (2019), 35-52 [pdf]
  14. Infinite algebraic subgroups of the real Cremona group (with M. F. Robayo)
    Osaka J. of Math., vol.55, no.4 (2018), 681-712 [pdf]
  15. The abelianisation of the real Cremona group
    Duke Math. J. vol. 167, no.2 (2018), 211-267 [pdf]
  16. Topological simplicity of the Cremona groups (with J. Blanc)
    Amer. J. Math. 140 (2018), no. 5, 1297-1309 [pdf]
  17. The decomposition group of a line (with I. Heden)
    Proc. Amer. Math. Soc. 145 (2017), no. 9, 3665-3680 [pdf]
  18. The Cremona group is compactly presented
    J. London Math. Soc. 93, no. 1 (2016), 25-46[pdf] [official page]

Thesis

Activities

Upcoming events

Past events

Talks

Upcoming talks

  • 16.-20.6.2025: Workshop on Cremona groups, University of Grenoble
  • 21.-25.7.2025: SRI Conference in Algebraic Geometry, Colorado - talk cancelled due to late pregnancy
  • 28.7. - 1.9.2025: 35th Brasilian Colloquium in Mathematics, IMPA - talk cancelled due to maternity leave

Recent talks

  • 28.10 - 1.11.2024: Birational Geometry and Number Theory, ICM Edinburgh
  • 8.2023: V ELGA, Brazil
  • 5.-8.5.2023: Algebraic Transformation Groups, Monte Verita, Switzerland
  • 30.10.-2.1.2023: Brill-Noether workshop, CIRM, Luminy
  • 20.9.2023: Séminaire “des Mathématiques” (Ens Ulm)
  • 21.-25.8.2023: 4th Korea-France Conference in Mathematics, KIAS, Korea
  • 19-21.6.2023: AGGITatE workshop
  • 23.6.2023: Seminaire Gémétrie, Bordeaux
  • 5.-9.6.2023: Birational Geometry and biregulous functions, Le Croisic, France
  • 15-17.5.2023: Spring meeting in Milano

Some recorded talks

ERC Saphidir and SERI

The project

The ERC Saphidir could not be transferred into Switzerland and therefore terminated on 14 Feburary 2025. The State Secretariat for Education, Research and Innovation (SERI) of Switzerland awarded me with replacement funding until December 2027.

The research group

Invited collaborators

Publications and preprints

  1. T. Duarte Guerreiro, L. Giovenzana, N. Viswanathan: On K-stability of P3 blown up along a smooth genus 2 curve of degree [arxiv] (12/2024)
  2. Eduardo Alves da Silva, Fernando Figueroa, Joaquín Moraga: Algebraic tori in the complement of quartic surfaces [arxiv] (11/2024)
  3. P. Fong and M. Maccan: Isotrivial elliptic surfaces in positive characteristic [arxiv] (05/2024)
  4. S. Zimmermann, Fabio Bernasconi, Andrea Fanelli and Julia Schneider: Explicit Sarkisov program for regular surfaces over arbitrary fields and applications [pdf] (04/2024)
  5. S. Zimmermann and R. Terpereau: Real forms of Mori fiber spaces with many symmetries [arxiv] (03/2024)
  6. Eduardo Alves da Silva: Birational geometry of Calabi-Yau pairs (P3,D) of coregularity 2[arxiv] (02/2024)
  7. Eduardo Alves da Silva: On the decomposition group of a nonsingular plane cubic by a log Calabi-Yau geometrical perspective[arxiv] (02/2024)
  8. E. Alves da Silva: On the decomposition group of a nonsingular plane cubic by a log Calabi-Yau geometrical perspective [arXiv] (02/2024)
  9. A. Fanelli, E. Floris , S. Zimmermann: Maximal subgroups in the Cremona groups [pdf] (11/2023)
  10. P. Fong: Automorphism groups of \PP^1-bundles over ruled surfaces, [pdf] (10/2023)
  11. S. Zimmermann: Survey on normal subgroups of Cremona groups [pdf] (06/2023)
  12. A. Boitrel: Del Pezzo surfaces of degree 5 over perfect fields [arxiv] (04/2023)

Events supported by ERC Saphidir and SERI

Teaching Uni Basel

Geometrie FS2025

Outreach

Outreach

Media in which I appear

Hands on maths

Visualize relations among Sarkisov links

Visualize relations among Sarkisov links over a perfect field [here] and [here] on the hompage of Stéphane Lamy.

Decompose birational maps of the plane

This is program created by Thibault Chailleux in his [master thesis]. It decomposes any birational map of the complex projective plane into quadratic maps.
Due to long computation time I limited the degree to < 31. Let me know if you need me to increase the limit.

Here is how it works:

  • Crate the map and decompose :
    • Give it a name (f,g,...).
    • Pick a letter used for the base-points (choose p if you want to name your points p0, p1, p2,...).
    • Choose the degree of your transformation. Due to long computation time I limited the degree to < 31.
    • Press "Compute transformation". It lists all possible characteristics for your chosen degree. Pick one and press "Compute transformation" again.
    • Choose which base-points you want to be infinitely near whom. The points are automatically ordered so that p_i can only be infinitely near p_j, j< i.
    • Press "Add transformation". It safes it on the right-hand side, where you also get its decomposition into quadratic transformations. You have now finished creating the transformation.
  • If you have created more than one transformation, you can choose under "Transformation" which map you want to see a decomposition of.
  • Compose transformations from the right-hand side:
    • Choose a name of your decomposition (f,g,...) that you have not used yet.
    • Under "Sub transformation" you can choose any of the transformations you have created.
    • The list below contains your chosen map and the quadratic transformations from the given decomposition.
    • Choose the maps in this list you want to compose. You may change the "sub-transformation" any time to add other maps to the composition.
    • Press "compute". You now find the decomposition in the list "Transformation".

    Create transformation

    Compose transformations

    compose :

    sub-transformations of

    Transformations details

    Decomposition details