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Trudy Mat. Inst. Steklova, 2009, Volume 264, Pages 184–208 (Mi tm799)  

This article is cited in 14 scientific papers (total in 14 papers)

Letters of a Bi-rationalist. VII Ordered Termination

V. V. Shokurovab

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

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 264, 178–200

Bibliographic databases:

UDC: 512.7
Received in August 2008

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
\by V.~V.~Shokurov
\paper Letters of a~Bi-rationalist. VII~Ordered Termination
\inbook Multidimensional algebraic geometry
\bookinfo Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences
\serial Trudy Mat. Inst. Steklova
\yr 2009
\vol 264
\pages 184--208
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2009
\vol 264
\pages 178--200

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    This publication is cited in the following articles:
    1. Fujino O., “Finite generation of the log canonical ring in dimension four”, Kyoto J. Math., 50:4 (2010), 671–684  crossref  mathscinet  zmath  isi  scopus
    2. 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  crossref  zmath  isi  scopus
    3. Shokurov V.V., Choi S.R., “Geography of log models: theory and applications”, Cent. Eur. J. Math., 9:3 (2011), 489–534  crossref  zmath  isi  elib  scopus
    4. Fujino O., “Fundamental theorems for the log minimal model program”, Publ. Res. Inst. Math. Sci., 47:3 (2011), 727–789  crossref  mathscinet  zmath  isi  scopus
    5. Birkar C., “On existence of log minimal models II”, J. Reine Angew. Math., 658 (2011), 99–113  crossref  mathscinet  zmath  isi  elib  scopus
    6. Birkar C., “On Existence of Log Minimal Models and Weak Zariski Decompositions”, Math. Ann., 354:2 (2012), 787–799  crossref  mathscinet  zmath  isi  elib  scopus
    7. Birkar C., “Existence of Log Canonical Flips and a Special Lmmp”, Publ. Math. IHES, 2012, no. 115, 325–368  crossref  mathscinet  zmath  isi  elib  scopus
    8. 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  crossref  mathscinet  zmath  isi  scopus
    9. Birkar C. Hu Zh., “Polarized Pairs, Log Minimal Models, and Zariski Decompositions”, Nagoya Math. J., 215 (2014), 203–224  crossref  mathscinet  zmath  isi  scopus
    10. Birkar C., Chen J.A., “Varieties Fibred Over Abelian Varieties With Fibres of Log General Type”, Adv. Math., 270 (2015), 206–222  crossref  mathscinet  zmath  isi  elib  scopus
    11. Brown M.V., Mckernan J., Svaldi R., Zong H.R., “A Geometric Characterization of Toric Varieties”, Duke Math. J., 167:5 (2018), 923–968  crossref  mathscinet  zmath  isi  scopus
    12. Hashizume K., “On the Non-Vanishing Conjecture and Existence of Log Minimal Models”, Publ. Res. Inst. Math. Sci., 54:1 (2018), 89–104  crossref  mathscinet  zmath  isi  scopus
    13. Hacon Ch. Moraga J., “On Weak Zariski Decompositions and Termination of Flips”, Math. Res. Lett., 27:5 (2020), 1393–1421  crossref  mathscinet  isi
    14. Yu. G. Prokhorov, “Equivariant minimal model program”, Russian Math. Surveys, 76:3 (2021), 461–542  mathnet  crossref  crossref  isi  elib
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