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arXiv · 1701.00027

Betti numbers and pseudoeffective cones in 2-Fano varieties

Giosuè Emanuele Muratore
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Abstract

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 $\ge n-2$, and also we complete the classification of weak 2-Fano varieties of Araujo and Castravet.

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Giosuè Emanuele Muratore. 2018-02-06. Betti numbers and pseudoeffective cones in 2-Fano varieties. https://doi.org/10.1515/advgeom-2021-0004

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