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
Invited collaborators
Publications and preprints
- P. Fong and M. Maccan: Isotrivial elliptic surfaces in positive characteristic [arxiv] (05/2024)
- S. Zimmermann, Fabio Bernasconi, Andrea Fanelli and Julia Schneider: Explicit Sarkisov program for regular surfaces over arbitrary fields and applications [pdf] (04/2024)
- S. Zimmermann and R. Terpereau: Real forms of Mori fiber spaces with many symmetries [arxiv] (03/2024)
- E. Alves da Silva: Birational geometry of Calabi-Yau pairs (P3,D) of coregularity 2 [arXiv] (02/2023)
- E. Alves da Silva: On the decomposition group of a nonsingular plane cubic by a log Calabi-Yau geometrical perspective [arXiv] (02/2023)
- 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)
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Supported events
- Thematic semester in 2025 on K-stability and birational geometry of real Fano threefolds
- Fano Varieties in Cetraro, 9-13 September 2024, Cetraro; organising with I. Cheltsov and A. Fanelli, supported by ERC Saphidir
- EpiGA conference 2024, 10 - 14 June 2024, Jussieu (Sorbonne University), Paris, organised with
S. Boucksom,
B. Claudon,
G. Pacienza and
C. Voisin
- 13th swiss-french workshop in Algebraic Geometry, 29 January - 2 February 2023, organised with A. Fanelli and J. Schneider
- Birational Geometry and Regulous Functions, 6-9 June 2023,
member of scientific committee
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