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- Volume 362 (2024)

- p. 1389-1397

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The theory of the Okounkov body is a usual tool for analyzing the asymptotic behaviour of the sectional ring of a line bundle over a projective manifold. In this note, combined with the algebraic reduction, we study the asymptotic behaviour of the sectional ring of a line bundle over any arbitrary compact, normal, irreducible complex space.

La théorie du corps d’Okounkov est un outil puissant pour analyser le comportement asymptotique de l’anneau canonique d’un fibré en droites sur une variété projective. Dans cette note, combiné avec la réduction algébrique, nous étudions le comportement asymptotique de l’anneau canonique d’un fibré en droites sur tout espace complexe compact, normal et irréductible arbitraire.

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Xiaojun Wu 1

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[1] Aldo Andreotti; Wilhelm Stoll Analytic and algebraic dependence of meromorphic functions, Lecture Notes in Mathematics, 234, Springer, 1971, iii+390 pages | DOI | MR | Zbl

[2] Sébastien Boucksom; Jean-Pierre Demailly; Mihai Păun; Thomas Peternell The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension, J. Algebr. Geom., Volume 22 (2013) no. 2, pp. 201-248 | DOI | MR | Zbl

[3] Sébastien Boucksom; Philippe Eyssidieux; Vincent Guedj; Ahmed Zeriahi Monge–Ampère equations in big cohomology classes, Acta Math., Volume 205 (2010) no. 2, pp. 199-262 | DOI | MR | Zbl

[4] Sébastien Boucksom; Charles Favre; Mattias Jonsson Differentiability of volumes of divisors and a problem of Teissier, J. Algebr. Geom., Volume 18 (2009) no. 2, pp. 279-308 | DOI | MR | Zbl

[5] Sébastien Boucksom Divisorial Zariski decompositions on compact complex manifolds, Ann. Sci. Éc. Norm. Supér., Volume 37 (2004) no. 1, pp. 45-76 | DOI | MR | Zbl | Numdam

[6] Frédéric Campana Orbifolds, special varieties and classification theory, Ann. Inst. Fourier, Volume 54 (2004) no. 3, pp. 499-630 | DOI | MR | Zbl | Numdam

[7] Frédéric Campana Réduction algébrique d’un morphisme faiblement Kählérien propre et applications, Math. Ann., Volume 256 (1981) no. 2, pp. 157-189 | DOI | MR | Zbl

[8] Frédéric Campana Sur les diviseurs non-polaires d’un espace analytique compact, J. Reine Angew. Math., Volume 332 (1982), pp. 126-133 | DOI | MR | Zbl

[9] Jean-Pierre Demailly; Lawrence Ein; Robert Lazarsfeld A subadditivity property of multiplier ideals. Dedicated to William Fulton on the occasion of his 60th birthday, Mich. Math. J., Volume 48 (2000), pp. 137-156 | DOI | MR | Zbl

[10] Jean-Pierre Demailly Analytic methods in algebraic geometry, Surveys of Modern Mathematics, 1, International Press; Higher Education Press, 2012, viii+231 pages | MR | Zbl

[11] Gerd Fischer; Otto Forster Ein Endlichkeitssatz für Hyperflächen auf kompakten komplexen Räumen, J. Reine Angew. Math., Volume 306 (1979), pp. 88-93 | MR | Zbl

[12] Heisuke Hironaka Resolution of singularities of an algebraic variety over a field of characteristic zero. I, Ann. Math., Volume 79 (1964), pp. 109-203 | DOI | MR | Zbl

[13] Heisuke Hironaka Resolution of singularities of an algebraic variety over a field of characteristic zero.II, Ann. Math., Volume 79 (1964), pp. 205-326 | DOI | MR | Zbl

[14] Heisuke Hironaka Flattening theorem in complex-analytic geometry, Am. J. Math., Volume 97 (1975), pp. 503-547 | DOI | MR | Zbl

[15] Shigeru Iitaka On D-dimensions of algebraic varieties, J. Math. Soc. Japan, Volume 23 (1971), pp. 356-373 | DOI | MR | Zbl

[16] Kiumars Kaveh; A. G. Khovanskii Newton–Okounkov bodies, semigroups of integral points, graded algebras and intersection theory, Ann. Math., Volume 176 (2012) no. 2, pp. 925-978 | DOI | MR | Zbl

[17] Robert Lazarsfeld; Mircea Mustaţă Convex bodies associated to linear series, Ann. Sci. Éc. Norm. Supér., Volume 42 (2009) no. 5, pp. 783-835 | DOI | MR | Zbl | Numdam

[18] Andrei Okounkov Why would multiplicities be log-concave?, The orbit method in geometry and physics (Marseille, 2000) (Progress in Mathematics), Volume 213, Birkhäuser, 2003, pp. 329-347 | MR | Zbl | DOI

[19] Andrei Okounkov Brunn–Minkowski inequality for multiplicities, Invent. Math., Volume 125 (1996) no. 3, pp. 405-411 | DOI | MR | Zbl

[20] Reinhold Remmert Meromorphe Funktionen in kompakten komplexen Räumen, Math. Ann., Volume 132 (1956), pp. 277-288 | DOI | MR | Zbl

[21] Walter Thimm Meromorphe Abbildungen von Riemannschen Bereichen, Math. Z., Volume 60 (1954), pp. 435-457 | DOI | MR | Zbl

[22] Kenji Ueno Classification theory of algebraic varieties and compact complex spaces. Notes written in collaboration with P. Cherenack, Lecture Notes in Mathematics, 439, Springer, 1975, xix+278 pages | MR | Zbl

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