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Invited talk

Monday, July 19, 13:30 ~ 14:30 UTC-3

Higher Fano Manifolds

Carolina Araujo

IMPA, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Fano manifolds are complex projective manifolds having positive first Chern class. The positivity condition on the first Chern class has far reaching geometric and arithmetic implications, making Fano manifolds a central subject in modern algebraic geometry. For instance, Fano manifolds are covered by rational curves, and families of Fano manifolds over one dimensional bases always admit holomorphic sections. In recent years, there has been great effort towards defining suitable higher analogues of the Fano condition. Higher Fano manifolds are expected to enjoy stronger versions of several of the nice properties of Fano manifolds. For instance, they should be covered by higher dimensional rational varieties, and families of higher Fano manifolds over higher dimensional bases should admit meromorphic sections (modulo Brauer obstruction). In this talk, I will discuss a possible notion of higher Fano manifolds in terms of positivity of higher Chern characters, and discuss special geometric features of these manifolds.

Joint work with Roya Beheshti (Washington University, USA), Ana-Maria Castravet (University of Versailles, France), Kelly Jabbusch (University of Michigan-Dearborn, USA), Svetlana Makarova (University of Pennsylvania, USA), Enrica Mazzon (Max Planck Institute, Germany), Libby Taylor (Stanford University, USA) and Nivedita Viswanathan (The University of Edinburgh, UK).

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