Seminar Algebra and Geometry: Giosuè Muratore (Roma-Strasbourg)

Betti numbers and pseudo effective cones in 2-Fano varieties

The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher dimensional analogous properties of Fano varieties. We propose a definition of (weak) k-Fano variety and conjecture the polyhedrality of the cone of pseudoeffective k-cycles for those varieties in analogy with the case k=1. Then, we calculate some Betti numbers of a large class of k-Fano varieties to prove some special case of the conjecture. In particular, the conjecture is true for all 2-Fano varieties of index ≥n-2, and also we complete the classification of weak 2-Fano varieties of Araujo and Castravet.

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