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 A sufficient condition for a toric weak Fano 4-fold to be deformed to a Fano manifold J. Korean Math. Soc. 2021 Vol. 58, No. 5, 1081-1107 https://doi.org/10.4134/JKMS.j190810Published online July 28, 2021Printed September 1, 2021 Hiroshi Sato 8-19-1, Nanakuma, Jonan-ku Abstract : In this paper, we introduce the notion of toric special weak Fano manifolds, which have only special primitive crepant contractions. We study their structure, and in particular completely classify smooth toric special weak Fano $4$-folds. As a result, we can confirm that almost every smooth toric special weak Fano $4$-fold is a weakened Fano manifold, that is, a weak Fano manifold which can be deformed to a Fano manifold. Keywords : Toric manifolds, weak Fano manifolds, deformation theory MSC numbers : Primary 14M25; Secondary 14D15, 14J45 Supported by : The author was partially supported by JSPS KAKENHI Grant Number JP18K03262. Downloads: Full-text PDF   Full-text HTML