Susanna Zimmermann

About Me


Full Professor
Institut de mathématiques d'Orsay, University of Paris-Saclay

Contact: susanna.zimmermannATSuniversite-paris-saclay.frS (take away the obvious letters)

Research interests: birational geometry, Cremona groups, algebraic groups, real algebraic geometry
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CV: english, français



Published articles

  1. 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.
  2. Factorization centers in dimension two and the Grothendieck ring of varieties (with Hsueh-Yung Lin and Evgeny Shinder), to appear in Algebraic Geometry [pdf]
  3. Small G-varieties (with Hanspeter Kraft and Andriy Regeta) to appear in Canadian J. of Math., 2024; 76(1), 173-215. [pdf][official page]
  4. A remark on Geiser involutions, Special New Zealand volume, Europ. J. of Math, 2022 [pdf] [official link]
  5. Bijective Cremona transformations of the plane (with Shamil Asgarli, Kuan-Wen Lai and Masahiro Nakahara), Selecta Math. New Ser. 28, 53 (2022)[pdf]
  6. Algebraic subgroups of the plane Cremona group over a perfect field (with Julia Schneider)
    EpiGA, vol. 5 (2021), no. 14 [pdf]
  7. Continuous automorphisms of Cremona groups (with Christian Urech)
    Int. J. of Math., vol. 32, no.4 (2021) [pdf]
  8. Quotients of higher dimensional Cremona groups (with J. Blanc and S. Lamy)
    Acta Math. Vol. 226, No. 2 (2021), pp. 211-318 [pdf]
  9. The real plane Cremona group is a non-trivial amalgam
    Annales de l'Institut Fourier, Volume 71 (2021) no. 3, pp. 1023-1045 [pdf]
  10. Signature morphisms from the Cremona group over a non-closed field (with S. Lamy)
    J. Eur. Math. Soc. 22 (2020), 3133-3173 [pdf]
  11. A new presentation of the plane Cremona group (with C. Urech)
    Proceedings of the AMS, vol. 147, no. 7 (2019) 2741-2755. [pdf]
  12. 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]
  13. Infinite algebraic subgroups of the real Cremona group (with M. F. Robayo)
    Osaka J. of Math., vol.55, no.4 (2018), 681-712 [pdf]
  14. The abelianisation of the real Cremona group
    Duke Math. J. vol. 167, no.2 (2018), 211-267 [pdf]
  15. Topological simplicity of the Cremona groups (with J. Blanc)
    Amer. J. Math. 140 (2018), no. 5, 1297-1309 [pdf]
  16. The decomposition group of a line (with I. Heden)
    Proc. Amer. Math. Soc. 145 (2017), no. 9, 3665-3680 [pdf]
  17. The Cremona group is compactly presented
    J. London Math. Soc. 93, no. 1 (2016), 25-46[pdf] [official page]



Upcoming events

  • 13th swiss-french workshop in Algebraic Geometry, 29 January - 2 February 2023, financial support by ERC Saphidir
  • K-Stability, Birational Geometry and Mirror Symmetry, Oberwolfach, 17-22 March 2024, with T. Delcroix and L. Heuberger
  • EpiGA conference, IHP, Paris, 10-14 June 2024
  • Birational Geometry and K-stability, 9-13 September 2024, Cetraro; organising with I. Cheltsov and A. Fanelli, supported by ERC Saphidir

Past events


Upcoming talks

  • 5.-8.5.2023: Algebraic Transformation Groups, Monte Verita, Switzerland
  • 8.2023: V ELGA, Brazil

Recent talks

  • 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

The project

Birational maps are key to classifying algebraic varieties, determining whether they are isomorphic. Sarkisov links are special birational maps describing Mori fibre spaces, but little is known about them over a field in high-dimensional spaces (from three and above). The ERC-funded Saphidir project will seek to describe all Sarkisov links in any dimension and in non-classical settings. Focus will be placed on classifying Sarkisov links over the field of complex numbers and over a field of positive characteristic.

The research group

Publications and preprints

  • A. Fanelli, E. Floris , S. Zimmermann: Maximal subgroups in the Cremona groups [pdf] (11/2023)
  • P. Fong: Automorphism groups of \PP^1-bundles over ruled surfaces, [pdf] (10/2023)
  • S. Zimmermann: Survey on normal subgroups of Cremona groups [pdf] (06/2023)
  • A. Boitrel: Del Pezzo surfaces of degree 5 over perfect fields [arxiv] (04/2023)

Supported events

  • Birational Geometry and K-stability, 9-13 September 2024, Cetraro,
    organising with I. Cheltsov and A. Fanelli
  • EpiGA conference, Jussieu, Paris, 10-14 June 2024,
    member of organising team
  • 13th swiss-french workshop in Algebraic Geometry, 29 January - 2 February 2023
  • Birational Geometry and Regulous Functions, 6-9 June 2023,
    member of scientific committee



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