Threefolds with big and nef anticanonical bundles II
Tóm tắt
In a follow-up to our paper [Threefolds with big and nef anticanonical bundles I, Math. Ann., 2005, 333(3), 569–631], we classify smooth complex projective threefolds Xwith −K
X
big and nef but not ample, Picard number γ(X) = 2, and whose anticanonical map is small. We assume also that the Mori contraction of X and of its flop X
+ are not both birational.
Tài liệu tham khảo
Arbarello E., Cornalba M., Griffiths P.A., Harris J., Geometry of Algebraic Curves, Grundlehren Math. Wiss., 267, Springer, New York, 1985
Bertini E., Introduzione alla Geometria Proiettiva degli Iperspazi, Enrico Spoerri, Pisa, 1907
Chel’tsov I.A., Bounded three-dimensional Fano varieties of integer index, Math. Notes, 1999, 66(3), 360–365
Hartshorne R., On the classification of algebraic space curves II, In: Algebraic Geometry, Brunswick, 1985, Proc. Sympos. Pure Math., 46(1), AMS, Providence, 1987, 145–164
Iskovskikh V.A., Double projection from a line onto Fano threefolds of the first kind, Math. USSR-Sb., 1990, 66(1), 265–284
Iskovskikh V.A., Prokhorov Yu.G., Fano Varieties, Encyclopaedia Math. Sci., 47, Springer, Berlin, 1999
Jahnke P., Peternell T., Almost del Pezzo manifolds, Adv. Geom., 2008, 8(3), 387–411
Jahnke P., Peternell T., Radloff I., Threefolds with big and nef anticanonical bundles I, Math. Ann., 2005, 333(3), 569–631
Jahnke P., Radloff I., Gorenstein Fano threefolds with base points in the anticanonical system. Compos. Math., 2006, 142(2), 422–432
Jahnke P., Radloff I., Terminal Fano threefolds and their smoothings, Math. Z. (in press), DOI: 10.1007/s00209-010-0780-8
Kollár J., Flops, Nagoya Math. J., 1989, 113, 15–36
Kollár J., Flips, flops, minimal models, etc., In: Surv. Differ. Geom., 1, Lehigh University, Bethlehem, 1991, 113–199
Kollár J., Mori S., Birational Geometry of Algebraic Varieties, Cambridge Tracts in Math., 134, Cambridge University Press, Cambridge, 1998
Mori S., Threefolds whose canonical bundles are not numerically effective, Ann. of Math., 1982, 116(1), 133–176
Namikawa Y., Smoothing Fano 3-folds. J. Algebraic Geom., 1997, 6(2), 307–324
Przhyjalkowski V.V., Cheltsov I.A., Shramov K.A., Hyperelliptic and trigonal Fano threefolds, Izv. Math., 2005, 69(2), 365–421
Reid M., Minimal models of canonical 3-folds, In: Algebraic Varieties and Analytic Varieties, Tokyo, 1981, Adv. Stud. Pure Math., 1, North-Holland, Amsterdam, 1983, 131–180
Shin K.-H., 3-dimensional Fano varieties with canonical singularities. Tokyo J. Math., 1989, 12(2), 375–385
Takeuchi K., Some birational maps of Fano 3-folds, Compos. Math., 1989, 71(3), 265–283