Yunling Chen (Univ. Lorraine)
Titre : Uniqueness results of meromorphic mappings from hyperbolic perspectives

Résumé : The long-standing Kobayashi conjecture and Green-Griffiths-Lang conjecture predict the geometry of entire curves in (quasi-)hyperbolic varieties. In this talk, our study is set on a log pair, consisting of the blow-up of $\mathbb{P}^n\times\mathbb{P}^n$ along the complete intersection of two generic hypersurfaces and the corresponding strict transform. By adapting jet techniques developed notably by Green-Griffiths, Demailly, Diverio-Merker-Rousseau, we establish the existence of jet differentials vanishing along an ample divisor on above log pair. Then following Siu’s strategy of slanted vector fields, we generate sufficiently many differential equations to achieve the algebraic elimination of entire curves when the degrees of such two generic hypersurfaces are at least $2^{2n} 3^{2n}(n)^{2n+5}$. As an application, we explore the relation between hyperbolicity and uniqueness, which derives some (pseudo-)uniqueness results of meromorphic mappings in $\mathbb{P}^n\mathbb{C}$ sharing two different generic hypersurfaces of high degrees. This is a joint work with D. Brotbek and B. Cadorel.