Higher Fano manifolds

Abstract: 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. 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 a 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.

algebraic geometry

Audience: researchers in the topic

( chat | video )

Comments: The synchronous discussion for Enrica Mazzon’s talk is taking place not in zoom-chat, but at tinyurl.com/2022-02-18-em (and will be deleted after ~3-7 days).

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Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

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