An extension theorem for Kähler currents with analytic singularities
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 4, pp. 893-905.

We prove an extension theorem for Kähler currents with analytic singularities in a Kähler class on a complex submanifold of a compact Kähler manifold.

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.

@article{AFST_2014_6_23_4_893_0,
     author = {Tristan C. Collins and Valentino Tosatti},
     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},
     mrnumber = {3270428},
     zbl = {06374893},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1429/}
}
TY  - JOUR
AU  - Tristan C. Collins
AU  - Valentino Tosatti
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  - https://afst.centre-mersenne.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 Tristan C. Collins
%A Valentino Tosatti
%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 https://afst.centre-mersenne.org/articles/10.5802/afst.1429/
%R 10.5802/afst.1429
%G en
%F AFST_2014_6_23_4_893_0
Tristan C. Collins; Valentino Tosatti. An extension theorem for Kähler currents with analytic singularities. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 4, pp. 893-905. doi : 10.5802/afst.1429. https://afst.centre-mersenne.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 L 2 -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 L 2 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 n , 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

Cited by Sources: