Betti numbers and pseudoeffective cones in 2-Fano varieties

Author:

Muratore Giosuè Emanuele12

Affiliation:

1. Università Degli Studi Roma Tre, Dipartimento di Matematica e Fisica, Largo San Murialdo 1, 00146 Roma , Italy

2. Université de Strasbourg, CNRS, IRMA, 7 Rue René Descartes , 67000 Strasbourg , France

Abstract

Abstract The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher-dimensional analogous properties of Fano varieties. We consider (weak) k-Fano varieties 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 at least n − 2, and we complete the classification of weak 2-Fano varieties answering Questions 39 and 41 in [2].

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Reference32 articles.

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