RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Tr. Mat. Inst. Steklova, 2004, Volume 246, Pages 328–351 (Mi tm165)  

This article is cited in 23 scientific papers (total in 23 papers)

Letters of a Bi-rationalist V: Mld's and Termination of Log Flips

V. V. Shokurov

Johns Hopkins University

Abstract: Termination of log flips and, more generally, of log quasiflips under the descending chain condition (dcc) of boundary multiplicities follows from two expected properties of the minimal log discrepancy (mld) function on algebraic log varieties: (1) the semicontinuity of mld's on any fixed log variety and (2) the ascending chain condition (acc) of mld's on the log varieties of given dimension with boundary multiplicities under the dcc. This reduces the global statement on termination to two local ones. All known cases of termination follow from this reduction. In particular, this gives the log termination in dimension 3, as well as the special and canonical termination up to dimension 4. To prove the log termination in dimension 4, one only needs the acc in dimension 4 for the mld values in the interval $[0,1]$.

Full text: PDF file (293 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 246, 315–336

Bibliographic databases:
UDC: 512.7
Received in February 2004

Citation: V. V. Shokurov, “Letters of a Bi-rationalist V: Mld's and Termination of Log Flips”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Tr. Mat. Inst. Steklova, 246, Nauka, MAIK Nauka/Inteperiodika, M., 2004, 328–351; Proc. Steklov Inst. Math., 246 (2004), 315–336

Citation in format AMSBIB
\Bibitem{Sho04}
\by V.~V.~Shokurov
\paper Letters of a~Bi-rationalist V: Mld's and Termination of Log Flips
\inbook Algebraic geometry: Methods, relations, and applications
\bookinfo Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences
\serial Tr. Mat. Inst. Steklova
\yr 2004
\vol 246
\pages 328--351
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm165}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2101303}
\zmath{https://zbmath.org/?q=an:1107.14012}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 246
\pages 315--336


Linking options:
  • http://mi.mathnet.ru/eng/tm165
  • http://mi.mathnet.ru/eng/tm/v246/p328

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. McKernan J., Prokhorov Yu., “Threefold thresholds”, Manuscripta Math., 114:3 (2004), 281–304  crossref  mathscinet  zmath  isi  scopus
    2. V. A. Iskovskikh, V. V. Shokurov, “Birational models and flips”, Russian Math. Surveys, 60:1 (2005), 27–94  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Fujino O., “On termination of 4-fold semi-stable log flips”, Publ. Res. Inst. Math. Sci., 41:2 (2005), 281–294  crossref  mathscinet  zmath  isi  scopus
    4. Alexeev V., Hacon Ch., Kawamata Yu., “Termination of (many) 4-dimensional log flips”, Invent. Math., 168:2 (2007), 433–448  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Birkar C., “Ascending chain condition for log canonical thresholds and termination of log flips”, Duke Math. J., 136:1 (2007), 173–180  crossref  mathscinet  zmath  isi  elib  scopus
    6. Kawakita M., “On a comparison of minimal log discrepancies in terms of motivic integration”, J. Reine Angew. Math., 620 (2008), 55–65  crossref  mathscinet  zmath  isi  scopus
    7. V. V. Shokurov, “Letters of a Bi-rationalist. VII Ordered Termination”, Proc. Steklov Inst. Math., 264 (2009), 178–200  mathnet  crossref  mathscinet  isi  elib  elib
    8. Birkar C., “Log minimal models according to Shokurov”, Algebra Number Theory, 3:8 (2009), 951–958  crossref  mathscinet  zmath  isi  scopus
    9. Ein L., Mustata M., “Jet Schemes and Singularities”, Proceedings of Symposia in Pure Mathematics: Algebraic Geometry Seattle 2005, Proceedings of Symposia in Pure Mathematics, 80, no. 1- 2, 2009, 505–546  crossref  mathscinet  zmath  isi
    10. Kovacs S.J., “Young person's guide to moduli of higher dimensional varieties”, Proceedings of Symposia in Pure Mathematics: Algebraic Geometry Seattle 2005, Proceedings of Symposia in Pure Mathematics, 80, no. 1- 2, 2009, 711–743  crossref  mathscinet  zmath  isi
    11. Birkar C., Cascini P., Hacon Ch.D., McKernan J., “Existence of minimal models for varieties of log general type”, J. Amer. Math. Soc., 23:2 (2010), 405–468  crossref  zmath  isi  scopus
    12. Birkar C., Shokurov V.V., “Mld's vs thresholds and flips”, J. Reine Angew. Math., 638 (2010), 209–234  crossref  mathscinet  zmath  isi  elib  scopus
    13. Birkar C., “On termination of log flips in dimension four”, Math. Ann., 346:2 (2010), 251–257  crossref  mathscinet  zmath  isi  scopus
    14. Birkar C., “On existence of log minimal models”, Compos Math, 146:4 (2010), 919–928  crossref  mathscinet  zmath  isi  scopus
    15. Kawakita M., “Towards Boundedness of Minimal Log Discrepancies by the Riemann-Roch Theorem”, Amer J Math, 133:5 (2011), 1299–1311  crossref  mathscinet  zmath  isi  scopus
    16. Totaro B., “The Acc Conjecture for Log Canonical Thresholds [After de Fernex, Ein, Mustata, Kollar]”, Asterisque, 2011, no. 339, 371+  mathscinet  zmath  isi
    17. 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
    18. Kawakita M., “Discreteness of Log Discrepancies Over Log Canonical Triples on a Fixed Pair”, J. Algebr. Geom., 23:4 (2014), 765–774  crossref  mathscinet  zmath  isi  scopus
    19. Kawakita M., “a Connectedness Theorem Over the Spectrum of a Formal Power Series Ring”, Int. J. Math., 26:11 (2015), 1550088  crossref  mathscinet  zmath  isi  scopus
    20. Nakamura Yu., “on Semi-Continuity Problems For Minimal Log Discrepancies”, J. Reine Angew. Math., 711 (2016), 167–187  crossref  mathscinet  zmath  isi  scopus
    21. Nakamura Yu., “On minimal log discrepancies on varieties with fixed Gorenstein index”, Mich. Math. J., 65:1 (2016), 165–187  crossref  mathscinet  zmath  isi  elib  scopus
    22. Lehn Ch., Pacienza G., “Deformations of Singular Symplectic Varieties and Termination of the Log Minimal Model Program”, Algebraic Geom., 3:4 (2016), 392–406  crossref  mathscinet  zmath  isi  scopus
    23. Kawakita M., “Divisors Computing the Minimal Log Discrepancy on a Smooth Surface”, Math. Proc. Camb. Philos. Soc., 163:1 (2017), 187–192  crossref  mathscinet  zmath  isi  scopus
  •    . . .  Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:613
    Full text:249
    References:37

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020