Algebraic models of the Euclidean plane

Autor: Jérémy Blanc, Adrien Dubouloz

Publikováno v: Épijournal de Géométrie Algébrique, Vol Volume 2 (2018)

We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic sur

Externí odkaz: https://doaj.org/article/64abbd42d4ed4c1f9fc7d7a30f3d94e6

Dynamical degrees of affine-triangular automorphisms of affine spaces

Autor: Jérémy Blanc, Immanuel van Santen

Publikováno v: Ergodic Theory and Dynamical Systems. 42:3551-3592

We study the possible dynamical degrees of automorphisms of the affine space$\mathbb {A}^n$. In dimension$n=3$, we determine all dynamical degrees arising from the composition of an affine automorphism with a triangular one. This generalizes the easi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b0c2453367d6f0b4dbd5b9d3a933ae0d
https://doi.org/10.1017/etds.2021.90

Non-rationality of some fibrations associated to Klein surfaces

Autor: Jérémy Blanc

We study the polynomial fibration induced by the equation of the Klein surfaces obtained as quotient of finite linear groups of automorphisms of the plane; this surfaces are of type A, D, E, corresponding to their singularities. The generic fibre of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::456f4cbe87582a00cd794ae1e5f0e9d3
http://doc.rero.ch/record/331816/files/13366_2013_Article_183.pdf

Embeddings of affine spaces into quadrics

Autor: Jérémy Blanc, Immanuel van Santen

Publikováno v: Transactions of the American Mathematical Society. 371:8429-8465

This article provides, over any field, infinitely many algebraic embeddings of the affine spaces $\mathbb{A}^1$ and $\mathbb{A}^2$ into smooth quadrics of dimension two and three respectively, which are pairwise non-equivalent under automorphisms of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d2e759d8f7238f79ecf678c1f2467b5d
https://doi.org/10.1090/tran/7555

Quotients of higher dimensional Cremona groups

Autor: Jérémy Blanc, Susanna Zimmermann, Stéphane Lamy

Publikováno v: Acta Mathematica
Acta Mathematica, 2021, ⟨10.4310/ACTA.2021.v226.n2.a1⟩
Acta Mathematica, Royal Swedish Academy of Sciences, Institut Mittag-Leffler, 2021, ⟨10.4310/ACTA.2021.v226.n2.a1⟩

We study large groups of birational transformations Bir(X), where X is a variety of dimension at least 3, defined over C or a subfield of C. Two prominent cases are when X is the projective space, in which case Bir(X) is the Cremona group of rank n,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a40ba195f32c644f699d51deedbbb2f6
https://hal.science/hal-01981369