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. 
@article{TM_2003_240_a3,
     author = {Yu. G. Prokhorov},
     title = {On the {Zariski} {Decomposition} {Problem}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {43--72},
     publisher = {mathdoc},
     volume = {240},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2003_240_a3/}
}
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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/