Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Betti numbers and pseudoeffective cones in 2-Fano varieties

Betti numbers and pseudoeffective cones in 2-Fano varieties AbstractThe 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]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

Betti numbers and pseudoeffective cones in 2-Fano varieties

Muratore, Giosuè Emanuele
Advances in Geometry , Volume 21 (4): 10 – Oct 26, 2021
Download PDF
10 pages

Loading next page...
 
/lp/de-gruyter/betti-numbers-and-pseudoeffective-cones-in-2-fano-varieties-9IYc2C3GTG
Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
eISSN
1615-715X
DOI
10.1515/advgeom-2021-0004
Publisher site
See Article on Publisher Site

Abstract

AbstractThe 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].

Journal

Advances in Geometry – de Gruyter

Published: Oct 26, 2021

Keywords: Fano variety; Betti number; cycle; Primary 14J45; Secondary 14M15

There are no references for this article.