PD Dr. Immanuel van Santen

About me

I am a Privatdozent (PD) in the Department of Mathematics and Computer Science at the University of Basel. Since October 2024, I am also a research associate in the Department of Mathematics and Statistics at the University of Bern.

My research subject lies in the field of algebraic geometry. I am particularly interested in the group of automorphisms/birational transformations of algebraic varieties and embedding problems of algebraic varieties. The rich automorphism groups and birational transformation groups of highly symmetric varieties is a very fascinating active research area.

Workshop "Algebraic Transformation Groups"

Together with Jérémy Blanc and Andriy Regeta, I organized a workshop on algebraic transformation groups in Monte Verità, Ascona, from May 5th to May 8th, 2024. Here is the webpage of the workshop.

Teaching in the autum term 2025 (University of Bern)

Lecture: Bachelorvorlesung: Mathematik I für Naturwissenschaften

Teaching in the spring term 2025 (University of Bern)

Lecture: Mastervorlesung: Galois Theory

Teaching in the autumn term 2024 (University of Basel)

Lecture: Hauptvorlesung: Lineare Algebra I
Lecture: Vorlesung: Einführung in die Topologie

Teaching in the spring term 2023 (University of Basel)

Lecture: Mastervorlesung: Algebraische Geometrie II

Teaching in the spring term 2022 (University of Basel)

Lecture: Hauptvorlesung: Algebra II

Teaching in the autumn term 2021 (University of Basel)

Lecture: Seminar: Differentialgeometrie

Teaching in the spring term 2021 (University of Basel)

Lecture: Hauptvorlesung: Differentialgeometrie

Teaching in the spring term 2020 (University of Basel)

Lecture: Hauptvorlesung: Algebra II

Teaching in the autumn term 2018 (University of Basel)

Lecture: Mastervorlesung: Algebraische Geometrie I

Teaching in the spring term 2018 (University of Basel)

Lecture: Hauptvorlesung: Algebra II

Teaching in the spring term 2015 (Jacobs University, Bremen)

Lecture: Bachelorvorlesung: Discrete Mathematics

Ph.D. student, coadvising together with Jérémy Blanc (University of Basel)

Sept 2020- : Mani Esna-Ashari, subject: Finite subgroups of Cremona groups

Master students (University of Basel)

Februar-August 2024: Rahel Dohrau, title: Generic projections in affine geometry.
March-July 2020: Gianni Talarico, title: Kleiman’s Transversality Theorem and Applications.

Poster

Peter Feller and Immanuel van Santen.
Uniqueness of Embeddings of the Affine Line into Algebraic Groups.
link to the poster

Preprints

Harry Schmidt and Immanuel van Santen.
On the Manin-Mumford Theorem for Algebraic Groups.
Preprint, submitted, May 2023.
https://arxiv.org/abs/2305.10261

¹⁾Peter Feller and Immanuel Stampfli.
Holomorphically equivalent algebraic embeddings.
Preprint, October 2014.
http://arxiv.org/abs/1409.7319

Publications

Andriy Regeta, Christian Urech, and Immanuel van Santen.
Group Theoretical Characterizations of Rationality.
Invent. Math. (2025).
https://arxiv.org/abs/2409.07864 or Official webpage

Andriy Regeta, Christian Urech, and Immanuel van Santen.
The Structure of Algebraic Families of Birational Transformations.
Advances in Mathematics 476 (2025).
https://arxiv.org/abs/2409.06475 or Official webpage

Immanuel van Santen.
On the Weights of Root Subgroups of Affine Toric Varieties.
Transform. Groups (2025), published online first.
https://arxiv.org/abs/2403.14389 or Official webpage

Andriy Regeta and Immanuel van Santen.
Maximal commutative unipotent subgroups and a characterization of affine spherical varieties.
J. Eur. Math. Soc. (2025).
https://arxiv.org/abs/2112.04784 or Official webpage

Jérémy Blanc, Pierre-Marie Poloni, Immanuel van Santen.
Complements of hypersurfaces in projective spaces.
Journal de l’École polytechnique — Mathématiques 11 (2024), 733-768.
https://arxiv.org/abs/2301.13040 or Official webpage

Peter Feller and Immanuel van Santen.
Existence of Embeddings of Smooth Varieties into Linear Algebraic Groups.
J. Algebraic Geom. 32 (2023), no. 4, 729-786.
https://arxiv.org/abs/2007.16164 or Official webpage

Jérémy Blanc and Immanuel van Santen.
Automorphisms of the affine 3-space of degree 3.
Indiana Univ. Math. J. 71 (2022), 857-912.
https://arxiv.org/abs/1912.02144 or Official webpage

Jérémy Blanc and Immanuel van Santen.
Dynamical degrees of affine-triangular automorphisms of affine spaces.
Ergodic Theory and Dynamical Systems (2021), 1–42.
https://arxiv.org/abs/1912.01324 or Official webpage

Andriy Regeta and Immanuel van Santen.
Characterizing Smooth Affine Spherical Varieties via the Automorphism Group.
Journal de l’École polytechnique — Mathématiques 8 (2021), 379–414.
https://arxiv.org/abs/1911.10896 or Official webpage

Hanspeter Kraft, Andriy Regeta and Immanuel van Santen.
Is the affine space determined by its automorphism group?
Int. Math. Res. Not. IMRN (2021), no. 6, 4280–4300.
https://arxiv.org/abs/1707.06883 or Official webpage

Peter Feller and Immanuel van Santen.
Uniqueness of Embeddings of the Affine Line into Algebraic Groups.
J. Algebraic Geom. 28 (2019), no. 4, 649–698.
https://arxiv.org/abs/1609.02113 or Official webpage

Jérémy Blanc and Immanuel van Santen.
Embeddings of Affine Spaces into Quadrics.
Trans. Amer. Math. Soc. 371 (2019), no. 12, 8429–8465.
https://arxiv.org/abs/1702.00779 or Official webpage

Stefan Maubach and Immanuel Stampfli.
On Maximal Subalgebras.
J. Algebra 483 (2017), 1–36.
http://arxiv.org/abs/1501.03753 or Official webpage

Immanuel Stampfli.
Algebraic embeddings of ℂ into SL_n(ℂ).
Transform. Groups 22 (2017), no. 2, 525–535.
https://arxiv.org/abs/1505.03735 or Official webpage

Immanuel Stampfli.
Automorphisms of ℂ³ Commuting with a ℂ⁺-Action.
Int. Math. Res. Not. IMRN (2015), no. 19, 9832–9856.
https://arxiv.org/abs/1406.6246 or Official webpage

Jérémy Blanc and Immanuel Stampfli.
Automorphisms of the Plane Preserving a Curve.
Algebr. Geom. 2 (2015), no. 2, 193–213.
https://arxiv.org/abs/1304.2549 or Official webpage

Immanuel Stampfli.
A note on Automorphisms of the Affine Cremona Group.
Math. Res. Lett. 20 (2013), no. 6, 1177–1181.
https://arxiv.org/abs/1209.3427 or Official webpage

Hanspeter Kraft and Immanuel Stampfli.
On Automorphisms of the Affine Cremona Group.
Ann. Inst. Fourier (Grenoble) 63 (2013), no. 3, 1137–1148.
https://arxiv.org/abs/1105.3739 or Official webpage

Immanuel Stampfli.
On the Topologies on ind-Varieties and related Irreducibility Questions.
J. Algebra 372 (2012), 531–541.
https://arxiv.org/abs/1109.4088 or Official webpage

Habilitation

Immanuel van Santen.
Embeddings and Automorphisms in Affine Algebraic Geometry. 2021.
Habilitation Thesis , Inaugural lecture , Lecture for the faculty

Dissertation

Immanuel Stampfli.
Contributions to Automorphisms of Affine Spaces. 2013.
Doctoral Thesis

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^{1) After uploading this article on arXiv.org, we were informed that the main result was already proven by Shulim Kaliman in https://arxiv.org/abs/1309.3791 now published in [Proc. Amer. Math. Soc.]. We don't intend to submit this article to any peer-review journal. ↩}