Abstract
(0.1) This paper applies the ideas of Mori theory [4] to toric varieties. Let X be a projective tonic variety (over any field) constructed from a simplicial fan F. The cone of effective 1-cycles NE(X) is polyhedral (1.7), spanned by the 1-strata l w ⊂ X; the condition that a 1-stratum l w gives an extremal ray R = Q + l w of NE(X) has a nice interpretation (2.10) in terms of the geometry of F around the wall w.
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References
V. Danilov, The geometry of toric varieties, Uspekhi Mat. Nauk 33: 2(1978), 85-134 = Russian Math Surveys 33: 2 (1978), 97 - 154.
V. Danilov, Birational geometry of tonic 3-folds,Izv. Akad. Nauk SSSR ser. Mat., 46 (1982), 971-982 = math USSR Izvestija, to appear.
T. Oda, Torus embeddings and applications, Tata Inst. Lect. Notes, Springer 1978.
S. Mori, Three-folds whose canonical bundles are not numerically effective, Ann. of Math. (2) 116 (1982), 133 - 176.
M. Reid, Canonical 3-folds, in Proc. Journées de Géom. Alg. Angers, Ed. A. Beauville, Sijthoff and Noordhoff, Alphen, 1980, 273 - 310.
M. Reid, Minimal models of canonical 3-folds, to appear in Advanced Studies in Pure Math. 1, eds. S. Iitaka and H. Morikawa, Kinokuniya and North-Holland, 1982.
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To I.R. Shafarevich on his 60th birthday
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© 1983 Springer Science+Business Media New York
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Reid, M. (1983). Decomposition of Toric Morphisms. In: Artin, M., Tate, J. (eds) Arithmetic and Geometry. Progress in Mathematics, vol 36. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-9286-7_15
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DOI: https://doi.org/10.1007/978-1-4757-9286-7_15
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3133-8
Online ISBN: 978-1-4757-9286-7
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