8 papers
Relative -Contractibility of Smooth Schemes
Adrien Dubouloz, Krishna Kumar Madhavan Vijayalakshmi, Paul Arne Ãstvær
We study smooth morphisms that are -contractible in the unstable -homotopy category . For base schemes of finite…
Cylinders in weighted Fano varieties
Adrien Dubouloz, In-Kyun Kim, Takashi Kishimoto +1
Cylinders in Fano varieties receives a lot of attentions recently from the viewpoints of birational geometry and unipotent geometry. In this article, we provide a survey of several…
On K-stability of singular hyperelliptic Fano 3-folds
Hamid Abban, Ivan Cheltsov, Adrien Dubouloz +3
We study the K-stability of singular Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system is base-point-free but not very ample.
Topologically integrable derivations and additive group actions on affine ind-schemes
Roberto Diaz, Adrien Dubouloz, Alvaro Liendo
We develop a theory of additive group actions on affine ind-schemes through a purely algebraic and topological framework. Affine ind-schemes are described via complete, second-coun…
Punctured tubular neighborhoods and stable homotopy at infinity
Frédéric Déglise, Adrien Dubouloz, Paul Arne Ãstvær
In this revised version (August 2025), we add a survey of \infty-categorical (co)limits and a replacement lemma for higher functoriality (Lem. 1.4.5), a framework for explicit mode…
Algebraic families of higher dimensional -contractible affine varieties non-isomorphic to affine spaces
Adrien Dubouloz, Parnashree Ghosh
We construct algebraic families of smooth affine -contractible varieties of every dimension over fields of characteristic zero which are non-isomorphic to a…