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Tr. Mat. Inst. Steklova, 2003, Volume 240, Pages 43–72 (Mi tm382)  

This article is cited in 15 scientific papers (total in 15 papers)

On the Zariski Decomposition Problem

Yu. G. Prokhorov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We discuss different generalizations of the Zariski decomposition, relations between them, and connections with finite generation of divisorial algebras.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2003, 240, 37–65

Bibliographic databases:

UDC: 512.7
Received in September 2002

Citation: Yu. G. Prokhorov, “On the Zariski Decomposition Problem”, Birational geometry: Linear systems and finitely generated algebras, Collected papers, Tr. Mat. Inst. Steklova, 240, Nauka, MAIK Nauka/Inteperiodika, M., 2003, 43–72; Proc. Steklov Inst. Math., 240 (2003), 37–65

Citation in format AMSBIB
\Bibitem{Pro03}
\by Yu.~G.~Prokhorov
\paper On the Zariski Decomposition Problem
\inbook Birational geometry: Linear systems and finitely generated algebras
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2003
\vol 240
\pages 43--72
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm382}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1993748}
\zmath{https://zbmath.org/?q=an:1092.14024}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2003
\vol 240
\pages 37--65


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Iskovskikh, “b-Divisors and Functional Algebras According to Shokurov”, Proc. Steklov Inst. Math., 240 (2003), 4–15  mathnet  mathscinet  zmath
    2. V. A. Iskovskikh, “On Shokurov's Work Prelimiting Flips”, Proc. Steklov Inst. Math., 240 (2003), 16–36  mathnet  mathscinet  zmath
    3. Proc. Steklov Inst. Math., 240 (2003), 75–213  mathnet  mathscinet  zmath
    4. Boucksom S., Favre Ch., Jonsson M., “Differentiability of Volumes of Divisors and a Problem of Teissier”, Journal of Algebraic Geometry, 18:2 (2009), 279–308  crossref  mathscinet  zmath  isi
    5. 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
    6. 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
    7. Kueronya A., Maclean C., “Zariski Decomposition of B-Divisors”, Math. Z., 273:1-2 (2013), 427–436  crossref  mathscinet  zmath  isi  scopus
    8. Birkar C., Hu Zh., “Polarized Pairs, Log Minimal Models, and Zariski Decompositions”, Nagoya Math. J., 215 (2014), 203–224  crossref  mathscinet  zmath  isi  scopus
    9. Choi S.R., Park J., “Potentially non-klt locus and its applications”, Math. Ann., 366:1-2 (2016), 141–166  crossref  mathscinet  zmath  isi  elib  scopus
    10. Roe J., “Local positivity in terms of Newton–Okounkov bodies”, Adv. Math., 301 (2016), 486–498  crossref  mathscinet  zmath  isi  elib  scopus
    11. Cacciola S., Lopez A.F., Viviani F., “Moriwaki divisors and the augmented base loci of divisors on the moduli space of curves”, Mich. Math. J., 65:3 (2016), 533–546  crossref  mathscinet  zmath  isi  scopus
    12. Fulger M., Lehmann B., “Zariski decompositions of numerical cycle classes”, J. Algebr. Geom., 26:1 (2017), 43–106  crossref  mathscinet  zmath  isi  scopus
    13. Di Nezza E., Floris E., Trapani S., “Divisorial Zariski Decomposition and Some Properties of Full Mass Currents”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 17:4 (2017), 1383–1396  mathscinet  zmath  isi
    14. Choi S.R., Park J., Won J., “Okounkov Bodies and Zariski Decompositions on Surfaces”, Bull. Korean. Math. Soc., 54:5 (2017), 1677–1697  crossref  mathscinet  isi  scopus
    15. Choi S.R., Park J., Won J., “Okounkov Bodies Associated to Pseudoeffective Divisors II”, Taiwan. J. Math., 21:3 (2017), 601–620  crossref  mathscinet  zmath  isi  scopus
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