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NOTES ON TORIC VARIETIES FROM MORI THEORETIC VIEWPOINT, II

Part of: Special varieties Birational geometry

Published online by Cambridge University Press:  29 August 2018

OSAMU FUJINO  and
HIROSHI SATO
OSAMU FUJINO
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan email fujino@math.sci.osaka-u.ac.jp
HIROSHI SATO
Affiliation:
Department of Applied Mathematics, Faculty of Sciences, Fukuoka University, 8-19-1, Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan email hirosato@fukuoka-u.ac.jp
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Abstract

We give new estimates of lengths of extremal rays of birational type for toric varieties. We can see that our new estimates are the best by constructing some examples explicitly. As applications, we discuss the nefness and pseudo-effectivity of adjoint bundles of projective toric varieties. We also treat some generalizations of Fujita’s freeness and very ampleness for toric varieties.

MSC classification

Primary: 14M25: Toric varieties, Newton polyhedra
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)
Type
Article
Information
Nagoya Mathematical Journal , Volume 239 , September 2020 , pp. 42 - 75
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Copyright
© 2018 Foundation Nagoya Mathematical Journal

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