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

Hiroshi Sato

doi:10.4134/JKMS.j190810

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

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Toric manifolds weak Fano manifolds deformation theory

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초록

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.

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.

참고문헌 (17)

V. V. Batyrev, "On the classification of smooth projective toric varieties", Tohoku Math. J, 43(4), pp.569~585 (1991)[DOI]
V. V. Batyrev, "On the classification of toric Fano 4-folds", Journal of Mathematical Sciences, 94(1), pp.1021~1050 (1999), Springer Science and Business Media LLC[DOI]
C. Casagrande, "Contractible classes in toric varieties", Mathematische Zeitschrift, 243(1), pp.99~126 (2003), Springer Science and Business Media LLC[DOI]
D. A. Cox, "Toric varieties, Graduate Studies in Mathematics, 124" (2011), American Mathematical Society
O. Fujino, "Notes on toric varieties from Mori theoretic viewpoint", Tohoku Math. J., 55(4), pp.551~564 (2003)
O. Fujino, "Introduction to the toric Mori theory", Michigan Math. J, 52(3), pp.649~665 (2004)[DOI]
W. Fulton, "Introduction to Toric Varieties, Annals of Mathematics Studies, 131" (1993), Princeton University Press
R. Koelman, "The number of moduli of families of curves on toric surfaces", pp.1991
A. Laface, "On deformations of toric varieties", arXiv:1610.03455, ~
K. Matsuki, "Introduction to the Mori program, Universitext" (2002), Springer-Verlag
T. Minagawa, "On classication of weakened Fano 3-folds with B2(X) = 2", Proc. of Algebraic Geometry Symposium (2000)
T. Minagawa, "Global smoothing of singular weak Fano 3-folds", J. Math. Soc. Japan, 55(3), pp.695~711 (2003)[DOI]
T. Oda, "Convex bodies and algebraic geometry" (1988), Springer-Verlag
M. Reid, "Arithmetic and geometry, Vol. II", pp.395~418 (1983), Birkhauser
M. Reid, "Toward the classification of higher-dimensional toric Fano varieties", Tohoku Math. J., 52(3), pp.383~413 (2000)[DOI]
Hiroshi Sato, "The classification of smooth toric weakened Fano 3-folds", manuscripta mathematica, 109(1), pp.73~84 (2002), Springer Science and Business Media LLC[DOI]
Hiroshi Sato, "Remarks on toric manifolds whose Chern characters are positive", Communications in Algebra, 48(6), pp.2528~2538 (2020), Informa UK Limited[DOI]

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