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Tr. Mat. Inst. Steklova, 2003, Volume 240, Pages 43–72
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This article is cited in 16 scientific papers (total in 16 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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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
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\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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V. A. Iskovskikh, “b-Divisors and Functional Algebras According to Shokurov”, Proc. Steklov Inst. Math., 240 (2003), 4–15
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V. A. Iskovskikh, “On Shokurov's Work Prelimiting Flips”, Proc. Steklov Inst. Math., 240 (2003), 16–36
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Proc. Steklov Inst. Math., 240 (2003), 75–213
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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
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Birkar C., “On Existence of Log Minimal Models and Weak Zariski Decompositions”, Math. Ann., 354:2 (2012), 787–799
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Birkar C., “Existence of Log Canonical Flips and a Special Lmmp”, Publ. Math. IHES, 2012, no. 115, 325–368
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Kueronya A., Maclean C., “Zariski Decomposition of B-Divisors”, Math. Z., 273:1-2 (2013), 427–436
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Birkar C., Hu Zh., “Polarized Pairs, Log Minimal Models, and Zariski Decompositions”, Nagoya Math. J., 215 (2014), 203–224
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Choi S.R., Park J., “Potentially non-klt locus and its applications”, Math. Ann., 366:1-2 (2016), 141–166
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Roe J., “Local positivity in terms of Newton–Okounkov bodies”, Adv. Math., 301 (2016), 486–498
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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
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Fulger M., Lehmann B., “Zariski decompositions of numerical cycle classes”, J. Algebr. Geom., 26:1 (2017), 43–106
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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
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Choi S.R., Park J., Won J., “Okounkov Bodies and Zariski Decompositions on Surfaces”, Bull. Korean. Math. Soc., 54:5 (2017), 1677–1697
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Choi S.R., Park J., Won J., “Okounkov Bodies Associated to Pseudoeffective Divisors II”, Taiwan. J. Math., 21:3 (2017), 601–620
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Pereira J.V., Svaldi R., “Effective Algebraic Integration in Bounded Genus”, Algebraic Geom., 6:4 (2019), 454–485
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