V. V. Shokurov, “Letters of a Bi-rationalist. VII Ordered Termination”, Multidimensional algebraic geometry, Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 264, MAIK Nauka/Interperiodica, Moscow, 2009, 184–208; Proc. Steklov Inst. Math., 264 (2009), 178

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 264, Pages 184–208 (Mi tm799)

This article is cited in 16 scientific papers (total in 16 papers)

Letters of a Bi-rationalist. VII Ordered Termination

V. V. Shokurov^ab

^a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
^b Department of Mathematics, Johns Hopkins University, Baltimore, USA

Full-text PDF (339 kB) Citations (16)

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Abstract: To construct a resulting model in the LMMP, it is sufficient to prove the existence of log flips and their termination for some sequences. We prove that the LMMP in dimension $d-1$ and the termination of terminal log flips in dimension $d$ imply, for any log pair of dimension $d$, the existence of a resulting model: a strictly log minimal model or a strictly log terminal Mori log fibration, and imply the existence of log flips in dimension $d+1$. As a consequence, we prove the existence of a resulting model of 4-fold log pairs, the existence of log flips in dimension 5, and Geography of log models in dimension 4.

Received in August 2008

English version:
Proceedings of the Steklov Institute of Mathematics, 2009, Volume 264, Pages 178–200
DOI: https://doi.org/10.1134/S0081543809010192

Bibliographic databases:

Document Type: Article

UDC: 512.7

Language: Russian

Citation: V. V. Shokurov, “Letters of a Bi-rationalist. VII Ordered Termination”, Multidimensional algebraic geometry, Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 264, MAIK Nauka/Interperiodica, Moscow, 2009, 184–208; Proc. Steklov Inst. Math., 264 (2009), 178–200

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tm799

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Cycle of papers

Letters of a Bi-rationalist V: Mld's and Termination of Log Flips
V. V. Shokurov
Trudy Mat. Inst. Steklova, 2004, 246, 328–351
Letters of a Bi-rationalist. VII Ordered Termination
V. V. Shokurov
Trudy Mat. Inst. Steklova, 2009, 264, 184–208

This publication is cited in the following 16 articles:

Yu. G. Prokhorov, “Equivariant minimal model program”, Russian Math. Surveys, 76:3 (2021), 461–542
Hacon Ch. Moraga J., “On Weak Zariski Decompositions and Termination of Flips”, Math. Res. Lett., 27:5 (2020), 1393–1421
Brown M.V., Mckernan J., Svaldi R., Zong H.R., “A Geometric Characterization of Toric Varieties”, Duke Math. J., 167:5 (2018), 923–968
Hashizume K., “On the Non-Vanishing Conjecture and Existence of Log Minimal Models”, Publ. Res. Inst. Math. Sci., 54:1 (2018), 89–104
Brian Lehmann, Proceedings of Symposia in Pure Mathematics, 95, Surveys on Recent Developments in Algebraic Geometry, 2017, 1
Birkar C., Chen J.A., “Varieties Fibred Over Abelian Varieties With Fibres of Log General Type”, Adv. Math., 270 (2015), 206–222
Shigetaka Fukuda, “Note on Quasi-Numerically Positive Log Canonical Divisors”, Journal of Mathematics, 2015 (2015), 1
Birkar C. Hu Zh., “Polarized Pairs, Log Minimal Models, and Zariski Decompositions”, Nagoya Math. J., 215 (2014), 203–224
Demailly J.-P., Hacon Ch.D., Paun M., “Extension Theorems, Non-Vanishing and the Existence of Good Minimal Models”, Acta Math., 210:2 (2013), 203–259
Birkar C., “On Existence of Log Minimal Models and Weak Zariski Decompositions”, Math. Ann., 354:2 (2012), 787–799
Birkar C., “Existence of Log Canonical Flips and a Special Lmmp”, Publ. Math. IHES, 2012, no. 115, 325–368
Corti A., Kaloghiros A.-S., Lazie V., “Introduction to the Minimal Model Program and the existence of flips”, Bull. Lond. Math. Soc., 43:3 (2011), 415–448
Shokurov V.V., Choi S.R., “Geography of log models: theory and applications”, Cent. Eur. J. Math., 9:3 (2011), 489–534
Fujino O., “Fundamental theorems for the log minimal model program”, Publ. Res. Inst. Math. Sci., 47:3 (2011), 727–789
Birkar C., “On existence of log minimal models II”, J. Reine Angew. Math., 658 (2011), 99–113
Fujino O., “Finite generation of the log canonical ring in dimension four”, Kyoto J. Math., 50:4 (2010), 671–684

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

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