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Uspekhi Mat. Nauk, 2005, Volume 60, Issue 1(361), Pages 29–98 (Mi umn1388)  

This article is cited in 8 scientific papers (total in 9 papers)

Birational models and flips

V. A. Iskovskikha, V. V. Shokurovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Johns Hopkins University, Baltimore

Abstract: This survey treats two chapters in the theory of log minimal models, namely, the chapter on different notions of models in this theory and the chapter on birational flips, that is, log flips, mainly in dimension 3. Our treatment is based on ideas and results of the second author: his paper on log flips (and also on material from the University of Utah workshop) for the first chapter, and his paper on prelimiting flips (together with surveys of these results by Corti and Iskovskikh) for the second chapter, where a complete proof of the existence of log flips in dimension 3 is given. At present, this proof is the simplest one, and the authors hope that it can be understood by a broad circle of mathematicians.

DOI: https://doi.org/10.4213/rm1388

Full text: PDF file (835 kB)
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English version:
Russian Mathematical Surveys, 2005, 60:1, 27–94

Bibliographic databases:

Document Type: Article
UDC: 512.6
MSC: Primary 14E30; Secondary 14E05, 14E15, 14C20, 14J30
Received: 15.10.2004

Citation: V. A. Iskovskikh, V. V. Shokurov, “Birational models and flips”, Uspekhi Mat. Nauk, 60:1(361) (2005), 29–98; Russian Math. Surveys, 60:1 (2005), 27–94

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    This publication is cited in the following articles:
    1. A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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
    3. F. A. Bogomolov, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (obituary)”, Russian Math. Surveys, 64:5 (2009), 939–946  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. 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
    5. Vyacheslav V. Shokurov, Sung Rak Choi, “Geography of log models: theory and applications”, centr.eur.j.math, 2011  crossref  mathscinet  isi  scopus
    6. Sung Rak Choi, “On the dual of the mobile cone”, Math. Z, 2011  crossref  mathscinet  isi  scopus
    7. Choi S.R., “Duality of the Cones of Divisors and Curves”, Math. Res. Lett., 19:2 (2012), 403–416  crossref  mathscinet  zmath  isi  elib  scopus
    8. Batyrev V., Gagliardi G., “On the Algebraic Stringy Euler Number”, Proc. Amer. Math. Soc., 146:1 (2018), 29–41  crossref  mathscinet  zmath  isi  scopus
    9. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
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