Abstract
In this notes we classify toric Fano 4-folds having positive second Chern character.
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D.A. Cox, J.B. Little and H. Schenck. Toric varieties, to be publish by American Mathematical Society as part of their Graduate Studies in Mathematics series, available at http://www.cs.amherst.edu/_dac/toric.html.
V.V. Batyrev. On the classification of toric Fano 4-folds. J. Math. Sci.(New York), 94(1) (1999), 1021–1050.
W. Fulton. Introduction to toric varieties. Annals of Mathematics Studies, 131 (1993), Princeton University Press.
A.J. de Jong and J. Starr. Higher Fano manifolds and rational surfaces. Duke Math. J., 139(1) (2007), 173–183.
A.J. de Jong and J. Starr. A note on Fano manifolds whose second Chern character is positive, pre-print math.AG/0602644v1, (2006).
C. Araujo and A-M. Castravet. 2-Fano 3-folds, preprint.
C. Araujo and A-M. Castravet. Polarized minimal families of rational curves and higher Fano manifolds, to appear in American Journal of Mathematics, preprint math.AG/0906.5388v1, (2009).
V.V. Batyrev. Toroidal Fano 3-folds. Mathematics of the USSR Izvestiya, 19 (1982), 13–25.
M. Kreuzer and B. Nill. Classification of toric Fano 5-folds. Advances in geometry, 9(1) (2009), 85–97.
J. Kollár, Y. Miyaoka and S. Mori. Rational connectedness and boundedness of Fano manifolds. J. Differ. Geom., 36(3) (1992), 765–779.
J. Kollár, Y. Miyaoka and S. Mori. Rational curves on Fano varieties, in Classification of irregular varieties, minimal models and abelian varieties. Proc. Conf., Trento/Italy 1990, Lect. Notes Math. 1515, 100–105 (1992).
H. Sato. Toward the classification of higher-dimensional toric Fano varieties. Tôhoku Math. J. (2), 52(3) (2000), 383–413.
R. Hartshorne. Algebraic Geometry. Graduate texts in Math., Springer-Verlag, (1977).
H. Sato. The numerical class of a surface on a toric manifold, pre-print math.AG/11065949v1, (2011).
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Nobili, E.E. Classification of Toric 2-Fano 4-folds. Bull Braz Math Soc, New Series 42, 399–414 (2011). https://doi.org/10.1007/s00574-011-0022-7
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DOI: https://doi.org/10.1007/s00574-011-0022-7