Geography of log models: theory and applications
Vyacheslav Shokurov; Sung Choi
Open Mathematics (2011)
- Volume: 9, Issue: 3, page 489-534
- ISSN: 2391-5455
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topVyacheslav Shokurov, and Sung Choi. "Geography of log models: theory and applications." Open Mathematics 9.3 (2011): 489-534. <http://eudml.org/doc/269681>.
@article{VyacheslavShokurov2011,
abstract = {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.},
author = {Vyacheslav Shokurov, Sung Choi},
journal = {Open Mathematics},
keywords = {Minimal Model Program; Minimal model; Mori fibration; Minimal model program; Sarkisov link},
language = {eng},
number = {3},
pages = {489-534},
title = {Geography of log models: theory and applications},
url = {http://eudml.org/doc/269681},
volume = {9},
year = {2011},
}
TY - JOUR
AU - Vyacheslav Shokurov
AU - Sung Choi
TI - Geography of log models: theory and applications
JO - Open Mathematics
PY - 2011
VL - 9
IS - 3
SP - 489
EP - 534
AB - 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.
LA - eng
KW - Minimal Model Program; Minimal model; Mori fibration; Minimal model program; Sarkisov link
UR - http://eudml.org/doc/269681
ER -
References
top- [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 Zbl1094.14025
- [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 Zbl1210.14019
- [3] Brown G., Corti A., Zucconi F., Birational geometry of 3-fold Morifibre spaces, In: The Fano Conference, 2004, Univ. Torino, Turin, 235–275 Zbl1063.14019
- [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 Zbl0866.14007
- [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 Zbl0960.14017
- [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 Zbl1124.14020
- [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 Zbl0922.14026
- [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 Zbl1079.14023
- [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 Zbl0672.14006
- [14] Klee V, Some characterizations of convex polyhedra, Acta Math., 1959, 102(1–2), 79–107 http://dx.doi.org/10.1007/BF02559569 Zbl0094.16802
- [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 Zbl0981.14016
- [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 Zbl0926.14003
- [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 Zbl1159.14020
- [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 Zbl0948.14008
- [20] Sarkisov V.G., Birational automorphisms of conic bundles, Math. USSR-Izv, 1981, 17(4), 177–202 http://dx.doi.org/10.1070/IM1981v017n01ABEH001326 Zbl0466.14012
- [21] Sarkisov V.G., On conic bundle structures, Math. USSR-Izv, 1982, 20(2), 355–390 http://dx.doi.org/10.1070/IM1983v020n02ABEH001354 Zbl0593.14034
- [22] Shokurov V.V., The nonvanishing theorem, Math. USSR-Izv, 1986, 26(3), 591–604 http://dx.doi.org/10.1070/IM1986v026n03ABEH001160 Zbl0605.14006
- [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 Zbl0873.14014
- [26] Shokurov V.V., Prelimiting flips, Proc. Steklov Inst. Math., 2003, 240(1), 75–213 Zbl1082.14019
- [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 Zbl1312.14041
- [28] Zagorskii A.A., On three-dimensional conical bundles, Mat. Zametki., 1977, 21(6), 745–758 (in Russian) Zbl0369.14008
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