Asymptotic invariants of base loci  [ Invariants asymptotiques des lieux de base ]
Annales de l'Institut Fourier, Tome 56 (2006) no. 6, pp. 1701-1734.

Le but de cet article est de définir et d’étudier systématiquement quelques invariants asymptotiques associés aux lieux de base des fibrés en droites sur les variétés projectives lisses. Le comportement fonctionnel de ces invariants est lié au comportement ensembliste des lieux de base.

The purpose of this paper is to define and study systematically some asymptotic invariants associated to base loci of line bundles on smooth projective varieties. The functional behavior of these invariants is related to the set-theoretic behavior of base loci.

DOI : https://doi.org/10.5802/aif.2225
Classification : 14C20,  14B05,  14F17
Mots clés : lieu de base, invariants asymptotiques, idéaux multiplicateurs
@article{AIF_2006__56_6_1701_0,
     author = {Ein, Lawrence and Lazarsfeld, Robert and Musta\c t\u a, Mircea and Nakamaye, Michael and Popa, Mihnea},
     title = {Asymptotic invariants of base loci},
     journal = {Annales de l'Institut Fourier},
     pages = {1701--1734},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {6},
     year = {2006},
     doi = {10.5802/aif.2225},
     mrnumber = {2282673},
     zbl = {1127.14010},
     language = {en},
     url = {www.numdam.org/item/AIF_2006__56_6_1701_0/}
}
Ein, Lawrence; Lazarsfeld, Robert; Mustaţă, Mircea; Nakamaye, Michael; Popa, Mihnea. Asymptotic invariants of base loci. Annales de l'Institut Fourier, Tome 56 (2006) no. 6, pp. 1701-1734. doi : 10.5802/aif.2225. http://www.numdam.org/item/AIF_2006__56_6_1701_0/

[1] Bădescu, L. Algebraic surfaces, Universitext, Springer-Verlag, New York, 2001 | Zbl 0965.14001

[2] Bauer, T.; Küronya, A.; Szemberg, T. Zariski chambers, volumes, and stable base loci, J. reine angew. Math., Volume 576 (2004), pp. 209-233 | Article | MR 2099205 | Zbl 1055.14007

[3] Boucksom, S. Divisorial Zariski decompositions on compact complex manifolds, Ann. Sci. Ecole Norm. Sup. (4), Volume 37 (2004), pp. 45-76 | Numdam | Zbl 1054.32010

[4] Boucksom, S.; Demailly, J.-P.; Păun, M.; Peternell, T. The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension (Preprint math.AG/0405285)

[5] Bourbaki, N. Algèbre commutative. Éléments de mathématique, Chap. 1–7, Hermann, Paris, 1961-1965

[6] Castraveţ, A.-M.; Tevelev, J. Hilbert’s 14 -th problem and Cox rings (Preprint math.AG/0505337) | Zbl 05082084

[7] Cox, D. The homogeneous coordinate ring of a toric variety, J. Alg. Geom., Volume 4 (1995), pp. 17-50 | MR 1299003 | Zbl 0846.14032

[8] Cutkosky, S. D. Zariski decomposition of divisors on algebraic varieties, Duke Math. J., Volume 53 (1986), pp. 149-156 | Article | MR 835801 | Zbl 0604.14002

[9] Demailly, J.-P.; Ein, L.; Lazarsfeld, R. A subadditivity property of multiplier ideals, Michigan Math. J., Volume 48 (2000), pp. 137-156 | Article | MR 1786484 | Zbl 1077.14516

[10] Ein, L.; Lazarsfeld, R.; Mustaţă, M.; Nakamaye, M.; Popa, M. Asymptotic invariants of line bundles (Preprint math.AG/0505054)

[11] Ein, L.; Lazarsfeld, R.; Mustaţă, M.; Nakamaye, M.; Popa, M. Restricted volumes and asymptotic base loci (2005) (Preprint)

[12] Ein, L.; Lazarsfeld, R.; Smith, K. Uniform bounds and symbolic powers on smooth varieties, Invent. Math., Volume 144 (2001), pp. 241-252 | Article | MR 1826369 | Zbl 1076.13501

[13] Hu, Y.; Keel, S. Mori Dream Spaces and GIT, Michigan Math. J., Volume 48 (2000), pp. 331-348 | Article | MR 1786494 | Zbl 1077.14554

[14] Javier Elizondo, E.; Kurano, K.; Watanabe, K. The total coordinate ring of a normal projective variety, J. Algebra, Volume 276 (2004), pp. 625-637 | Article | MR 2058459 | Zbl 1074.14006

[15] Küronya, A. Volumes of line bundles (Preprint math. AG/0211404)

[16] Lazarsfeld, R. Positivity in algebraic geometry, I–II, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Volume 48–49, Springer-Verlag, Berlin, 2004 | MR 2095471 | Zbl 1066.14021

[17] Mustaţă, M. On multiplicities of graded sequences of ideals, J. Algebra, Volume 256 (2002), pp. 229-249 | Article | MR 1936888 | Zbl 1076.13500

[18] Nakamaye, M. Stable base loci of linear series, Math. Ann., Volume 318 (2000), pp. 837-847 | Article | MR 1802513 | Zbl 1063.14008

[19] Nakamaye, M. Base loci of linear series are numerically determined, Trans. Amer. Math. Soc., Volume 355 (2002), pp. 551-566 | Article | MR 1932713 | Zbl 1017.14017

[20] Nakayama, N. Zariski-decomposition and abundance, Math. Society of Japan Memoirs, Volume 14, Mathematical Society of Japan, Tokyo, 2004 | MR 2104208 | Zbl 1061.14018

[21] Tessier, B. Sur une inégalité de Minkowski pour les multiplicités, Appendix to a paper of D. Eisenbud and H.I. Levine, The degree of a C map germ, Ann. Math., Volume 106 (1977), pp. 38-44 | Zbl 0443.13010

[22] Wolfe, A. Asymptotic invariants of graded systems of ideals and linear systems on projective bundles (2005) (Ph. D. Thesis)