Nous démontrons un théorème d’extension pour les courants kählériens avec singularités analytiques dans une classe de Kähler sur une sous-variété complexe d’une variété kählérienne compacte.
We prove an extension theorem for Kähler currents with analytic singularities in a Kähler class on a complex submanifold of a compact Kähler manifold.
@article{AFST_2014_6_23_4_893_0, author = {Collins, Tristan C. and Tosatti, Valentino}, title = {An extension theorem for {K\"ahler} currents with analytic singularities}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {893--905}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 23}, number = {4}, year = {2014}, doi = {10.5802/afst.1429}, zbl = {06374893}, mrnumber = {3270428}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/afst.1429/} }
TY - JOUR AU - Collins, Tristan C. AU - Tosatti, Valentino TI - An extension theorem for Kähler currents with analytic singularities JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2014 SP - 893 EP - 905 VL - 23 IS - 4 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1429/ DO - 10.5802/afst.1429 LA - en ID - AFST_2014_6_23_4_893_0 ER -
%0 Journal Article %A Collins, Tristan C. %A Tosatti, Valentino %T An extension theorem for Kähler currents with analytic singularities %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2014 %P 893-905 %V 23 %N 4 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1429/ %R 10.5802/afst.1429 %G en %F AFST_2014_6_23_4_893_0
Collins, Tristan C.; Tosatti, Valentino. An extension theorem for Kähler currents with analytic singularities. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 23 (2014) no. 4, pp. 893-905. doi : 10.5802/afst.1429. http://archive.numdam.org/articles/10.5802/afst.1429/
[1] Collins (T.C.), Greenleaf (A.), Pramanik (M.).— A multi-dimensional resolution of singularities with applications to analysis, Amer. J. Math. 135, no. 5, p. 1179-1252 (2013). | MR | Zbl
[2] Collins (T.C.), V. Tosatti (V.).— Kähler currents and null loci, preprint, arXiv:1304.5216.
[3] Coltoiu (M.).— Traces of Runge domains on analytic subsets, Math. Ann. 290, p. 545-548 (1991). | MR | Zbl
[4] Coman (D.), Guedj (V.), Zeriahi (A.).— Extension of plurisubharmonic functions with growth control, J. Reine Angew. Math. 676, p. 33-49 (2013). | MR | Zbl
[5] Demailly (J.-P.).— Regularization of closed positive currents and intersection theory, J. Algebraic Geom. 1, no. 3, p. 361-409 (1992). | MR | Zbl
[6] Demailly (J.-P.), Păun (M.).— Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math., 159, no. 3, p. 1247-1274 (2004). | MR | Zbl
[7] Hisamoto (T.).— Remarks on -jet extension and extension of singular Hermitian metric with semi positive curvature, preprint, arXiv:1205.1953.
[8] Ohsawa (T.), Takegoshi (K.).— On the extension of holomorphic functions, Math. Z. 195, no. 2, p. 197-204 (1987). | MR | Zbl
[9] Ornea (L.), Verbitsky (M.).— Embeddings of compact Sasakian manifolds, Math. Res. Lett. 14, no. 4, p. 703-710 (2007). | MR | Zbl
[10] Phong (D.H.), Stein (E.M.), Sturm (J.).— On the growth and stability of real-analytic functions, Amer. J. Math. 121, no. 3, p. 519-554 (1999). | MR | Zbl
[11] Phong (D.H.), Sturm (J.).— Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions, Ann. of Math. (2) 152, no. 1, p. 277-329 (2000). | MR | Zbl
[12] Phong (D.H.), Sturm (J.).— On the algebraic constructibility of varieties of integrable rational functions on , Math. Ann. 323, no. 3, p. 453-484 (2002). | MR | Zbl
[13] Richberg (R.).— Stetige streng pseudokonvexe Funktionen, Math. Ann. 175, p. 257-286 (1968). | MR | Zbl
[14] Sadullaev (A.).— Extension of plurisubharmonic functions from a submanifold, Dokl. Akad. Nauk USSR 5, p. 3-4 (1982). | Zbl
[15] Schumacher (G.).— Asymptotics of Kähler-Einstein metrics on quasi-projective manifolds and an extension theorem on holomorphic maps, Math. Ann. 311, no. 4, p. 631-645 (1998). | MR | Zbl
[16] Siu (Y.-T.).— Every Stein subvariety admits a Stein neighborhood, Invent. Math. 38, no. 1, p. 89-100 (1976/77). | MR | Zbl
[17] Wu (D.).— Higher canonical asymptotics of Kähler-Einstein metrics on quasi-projective manifolds, Comm. Anal. Geom. 14, no. 4, p. 795-845 (2006). | MR | Zbl
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