Geodesic
On the Zariski Decomposition Problem
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Birational geometry: Linear systems and finitely generated algebras, Tome 240 (2003), pp. 43-72.

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We discuss different generalizations of the Zariski decomposition, relations between them, and connections with finite generation of divisorial algebras. 
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Yu. G. Prokhorov. On the Zariski Decomposition Problem. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Birational geometry: Linear systems and finitely generated algebras, Tome 240 (2003), pp. 43-72. http://geodesic.mathdoc.fr/item/TM_2003_240_a3/

[1] Benveniste X., “Sur la décomposition de Zariski en dimension $3$”, C. R. Acad. Sci. Paris. Sér. 1, 295:2 (1982), 107–110 | MR | Zbl

[2] Burbaki N., Kommutativnaya algebra, Mir, M., 1971 | MR

[3] Boucksom S., Higher dimensional Zariski decompositions, , 2002 http://jp.arxiv.org/ abs/math.AG/0204336

[4] Cutkosky S. D., “Zariski decomposition of divisors on algebraic varieties”, Duke Math. J., 53:1 (1986), 149–156 | DOI | MR | Zbl

[5] Demailly J.-P., Complex analytic and algebraic geometry, http://www-fourier. ujf-grenoble.fr/~demailly/manuscripts

[6] Fujino O., Mori S., “A canonical bundle formula”, J. Diff. Geom., 56:1 (2000), 167–188 | MR | Zbl

[7] Fujita T., “On Zariski problem”, Proc. Japan Acad. A., 55:3 (1979), 106–110 | DOI | MR | Zbl

[8] Fujita T., “Fractionally logarithmic canonical rings of algebraic surfaces”, J. Fac. Sci. Univ. Tokyo. Sect. IA, 30:3 (1984), 685–696 | MR | Zbl

[9] Fujita T., “Zariski decomposition and canonical rings of elliptic threefolds”, J. Math. Soc. Japan, 38:1 (1986), 19–37 | DOI | MR | Zbl

[10] Fujita T., “Approximating Zariski decomposition of big line bundles”, Kodai Math. J., 17:1 (1994), 1–3 | DOI | MR | Zbl

[11] Griffits F., Kharris Dzh., Printsipy algebraicheskoi geometrii, T. 1, 2, Mir, M., 1982 | MR

[12] Iskovskikh V. A., “b-Divizory i funktsionalnye algebry po Shokurovu”, Trudy MIAN, 8–20 | MR | Zbl

[13] Kawamata Y., “The Zariski decomposition of log-canonical divisors”, Algebraic geometry. Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Symp. Pure Math., 46, Amer. Math. Soc., Providence, RI, 1987, 425–433 | MR

[14] Kawamata Y., “Crepant blowing-up of $3$-dimensional canonical singularities and its application to degenerations of surfaces”, Ann. Math., 127:1 (1988), 93–163 | DOI | MR | Zbl

[15] Mori S., “Classification of higher-dimensional varieties”, Algebraic geometry. Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Symp. Pure Math., 46, Amer. Math. Soc., Providence, RI, 1987, 269–331 | MR

[16] Moriwaki A., “Semi-ampleness of the numerically effective part of Zariski decomposition”, J. Math. Kyoto Univ., 26:3 (1986), 465–481 | MR | Zbl

[17] Moriwaki A., “Semi-ampleness of the numerically effective part of Zariski decomposition, II”, Algebraic geometry and commutative algebra, v. 1, Kinokuniya, Tokyo, 1988, 289–311 | MR

[18] Nakayama N., Zariski decomposition and abundance, Preprint RIMS-1142 | MR

[19] Sakai F., “Weil divisors on normal surfaces”, Duke Math. J., 51:4 (1984), 877–887 | DOI | MR | Zbl

[20] Shokurov V. V., “Trekhmernye logperestroiki”, Izv. RAN. Ser. mat., 56:1 (1992), 105–201 ; 57:6 (1993), 141–175 | MR | Zbl | MR | Zbl

[21] Shokurov V. V., “Complements on surfaces”, J. Math. Sci., 102:2 (2000), 3876–3932 | DOI | MR | Zbl

[22] Shokurov V. V., “Prelimiting flips”, Trudy MIAN, 82–219 | MR | Zbl

[23] Tsuji H., “Analytic Zariski decomposition”, Proc. Japan Acad. A., 68:7 (1992), 161–163 | DOI | MR | Zbl

[24] Tsuji H., “Existence and applications of analytic Zariski decompositions”, Analysis and geometry in several complex variables (Katata, 1997), Trends Math., Birkhäuser, Boston, MA, 1999, 253–271 | MR | Zbl

[25] Zariski O., “The theorem of Riemann–Roch for high multiples of an effective divisor on an algebraic surface”, Ann. Math. Ser. 2, 76 (1962), 560–615 | DOI | MR | Zbl

[26] Wilson P. M. H., “On the canonical ring of algebraic varieties”, Compos. Math., 43:3 (1981), 365–385 | MR | Zbl