The Cremona group in dimension n is the subgroup of birational transformation of the projective space IP^n. Describing the structure of the Cremona group is a major problem in algebraic geometry. While the theory is well developed in dimension 2, little is known in dimension ≥3. A natural problem is to construct special subgroups of the Cremona group. In 2013, Blanc described the subgroup of the Cremona group of the plane that preserves the meromorphic volume form ω= (dx/x) ∧ (dy/y). The form ω has simple poles exactly along the 3 coordinate lines. The pair (IP^2, ω) is an example of a Calabi-Yau pair: a pair (X,D) where X is a complex projective variety, and D is the divisor associated to a meromorphic volume form on X. Calabi-Yau pairs appear naturally in the context of the Minimal Model Program, and have been much investigated.
In this talk, I will explain how one can explore the birational geometry of Calabi-Yau pairs to construct interesting subgroups of the Cremona group in dimension ≥3.
This is joint work with Alessio Corti (London, UK) and Alex Massarenti (Ferrara, Italy).
L’exposé sera retransmis via Zoom.
Nom de réunion : « Sem AG du LMV – Carolina Araujo » ; contacter Luc Pirio pour le mot de passe.