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2011 | 9 | 3 | 489-534
Tytuł artykułu

Geography of log models: theory and applications

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This is an introduction to geography of log models with applications to positive cones of Fano type (FT) varieties and to geometry of minimal models and Mori fibrations.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
3
Strony
489-534
Opis fizyczny
Daty
wydano
2011-06-01
online
2011-03-22
Twórcy
Bibliografia
  • [1] Ambro F., The moduli b-divisor of an lc-trivial fibration, Compos. Math., 2005, 141(2), 385–403 http://dx.doi.org/10.1112/S0010437X04001071
  • [2] Birkar C., Cascini P., Hacon C.D., McKernan J., Existence of minimal models for varieties of log general type, J. Amer. Math. Soc., 2010, 23(2), 405–468 http://dx.doi.org/10.1090/S0894-0347-09-00649-3
  • [3] Brown G., Corti A., Zucconi F., Birational geometry of 3-fold Morifibre spaces, In: The Fano Conference, 2004, Univ. Torino, Turin, 235–275
  • [4] Cheltsov I.A., Grinenko M.M., Birational rigidity is not an open property, preprint available at http://arxiv.org/abs/math/0612159
  • [5] Choi S., Geography of Log Models and its Applications, Ph.D. thesis, Johns Hopkins University, Baltimore, 2008
  • [6] Corti A., Factoring birational maps of threefolds after Sarkisov, J. Algebraic Geom., 1995, 4(2), 223–254
  • [7] Corti A., Singularities of linear systems and 3-fold birational geometry, In: Explicit Birational Geometry of 3-folds, London Math. Soc. Lecture Note Ser., 281, Cambridge University Press, Cambridge, 2000, 259–312
  • [8] Grinenko M.M., Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2, Sb. Math., 2000, 191(5–6), 633–653 http://dx.doi.org/10.1070/SM2000v191n05ABEH000475
  • [9] Grinenko M.M., Fibrations into del Pezzo surfaces, Russian Math. Surveys, 2006, 61(2), 255–300 http://dx.doi.org/10.1070/RM2006v061n02ABEH004312
  • [10] Iskovskih V.A., On the rationality problem for three-dimensional algebraic varieties fibered over del Pezzo surfaces, Trudy Mat. Inst. Steklov, 1995, 208, Teor. Chisel, Algebra i Algebr. Geom., 128–138
  • [11] Iskovskih V.A., A rationality criterion for conic bundles, Sb. Mat, 1996, 187(7), 1021–1038 http://dx.doi.org/10.1070/SM1996v187n07ABEH000145
  • [12] Iskovskikh V.A., Shokurov V.V., Birational models and flips, Russian Math. Surveys, 2005, 60(1), 27–94 http://dx.doi.org/10.1070/RM2005v060n01ABEH000807
  • [13] Kawamata Y, Matsuda K., Matsuki K., Introduction to the minimal model problem, In: Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987, 283–360
  • [14] Klee V, Some characterizations of convex polyhedra, Acta Math., 1959, 102(1–2), 79–107 http://dx.doi.org/10.1007/BF02559569
  • [15] Kollár J., Miyaoka Y, Mori S., Takagi H., Boundedness of canonical Q-Fano 3-folds Proc. Japan Acad. Ser. A Math. Sci., 2000, 76(5), 73–77 http://dx.doi.org/10.3792/pjaa.76.73
  • [16] Kollár J., Mori S., Birational Geometry of Algebraic Varieties, Cambridge Tracts in Math., 134, Cambridge University Press, Cambridge, 1998 http://dx.doi.org/10.1017/CBO9780511662560
  • [17] Park J., Birational maps of del Pezzo fibrations, J. Reine Angew. Math., 2001, 538, 213–221 http://dx.doi.org/10.1515/crll.2001.066
  • [18] Prokhorov Yu.G., Shokurov V.V., Towards the second main theorem on complements, J. Algebraic Geom., 2009, 18(1), 151–199
  • [19] Pukhlikov A.V., Birational automorphisms of three-dimensional algebraic varieties with a pencil of del Pezzo surfaces, Izv. Math., 1998, 62(1), 115–155 http://dx.doi.org/10.1070/IM1998v062n01ABEH000188
  • [20] Sarkisov V.G., Birational automorphisms of conic bundles, Math. USSR-Izv, 1981, 17(4), 177–202 http://dx.doi.org/10.1070/IM1981v017n01ABEH001326
  • [21] Sarkisov V.G., On conic bundle structures, Math. USSR-Izv, 1982, 20(2), 355–390 http://dx.doi.org/10.1070/IM1983v020n02ABEH001354
  • [22] Shokurov V.V., The nonvanishing theorem, Math. USSR-Izv, 1986, 26(3), 591–604 http://dx.doi.org/10.1070/IM1986v026n03ABEH001160
  • [23] Shokurov V.V., Three-dimensional log perestroikas, Izv. Ross. Akad. Nauk Ser. Mat, 1992, 56(1), 105–203
  • [24] Shokurov V.V., Anticanonical boundedness for curves, Appendix to: Nikulin V.V., The diagram method for 3-folds and its application to the Kähler cone and Picard number of Calabi-Yau 3-folds, In: Higher Dimensional Complex Varieties, Trento, June 1994, de Gruyter, Berlin, 1996, 321–328
  • [25] Shokurov V.V., 3-fold log models, J. Math. Sci., 1996, 81(3), 2667–2699 http://dx.doi.org/10.1007/BF02362335
  • [26] Shokurov V.V., Prelimiting flips, Proc. Steklov Inst. Math., 2003, 240(1), 75–213
  • [27] Shokurov V.V., Letters of a bi-rationalist. VII Ordered termination, Proc. Steklov Inst. Math., 2009, 264(1), 178–200 http://dx.doi.org/10.1134/S0081543809010192
  • [28] Zagorskii A.A., On three-dimensional conical bundles, Mat. Zametki., 1977, 21(6), 745–758 (in Russian)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0013-3
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