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J. Korean Math. Soc. 2021; 58(5): 1081-1107

Online first article July 28, 2021      Printed September 1, 2021

https://doi.org/10.4134/JKMS.j190810

Copyright © The Korean Mathematical Society.

A sufficient condition for a toric weak Fano 4-fold to be deformed to a Fano manifold

Hiroshi Sato

8-19-1, Nanakuma, Jonan-ku

Abstract

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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.

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