no. 3
Analytic inversion of adjunction: L 2 extension theorems with gain
[L’inversion analytique d’adjonction : théorèmes de prolongement avec gain]
McNeal, Jeffery D.1 ; Varolin, Dror2
1 Department of Mathematics 100 mathematics building 231 W. 18th avenue Columbus, Ohio 43210-1174 (USA)
2 Stony Brook University Department of Mathematics Stony Brook NY 11794-3651 (USA)
Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 703-718.

Nous établissons des résultats nouveaux sur le prolongement L 2 à poids des formes holomorphes de degré maximal avec des valeurs dans un fibré linéaire, d’une hypersurface holomorphe lisse définie par une fonction holomorphe. Les poids que nous employons sont déterminés par certaines fonctions que nous appelons des dénominateurs. Nous donnons une collection d’exemples de ces dénominateurs liés au diviseur défini par la sous-variété.

We establish new results on weighted L 2 -extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions that we call denominators. We give a collection of examples of these denominators related to the divisor defined by the submanifold.

DOI : 10.5802/aif.2273
Classification : 32A99, 32Q99
Keywords: Ohsawa-Takegoshi-type extension, twisted Bochner-Kodaira technique, denominators
Mot clés : Ohsawa-Takegoshi-type extension, technique de Bochner-Kodaira tordue, dénominateurs

McNeal, Jeffery D. 1 ; Varolin, Dror 2

1 Department of Mathematics 100 mathematics building 231 W. 18th avenue Columbus, Ohio 43210-1174 (USA)
2 Stony Brook University Department of Mathematics Stony Brook NY 11794-3651 (USA) 
@article{AIF_2007__57_3_703_0,
     author = {McNeal, Jeffery D. and Varolin, Dror},
     title = {Analytic inversion of adjunction: $L^2$ extension theorems with gain},
     journal = {Annales de l'Institut Fourier},
     pages = {703--718},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {57},
     number = {3},
     year = {2007},
     doi = {10.5802/aif.2273},
     mrnumber = {2336826},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2273/}
}
TY  - JOUR
AU  - McNeal, Jeffery D.
AU  - Varolin, Dror
TI  - Analytic inversion of adjunction: $L^2$ extension theorems with gain
JO  - Annales de l'Institut Fourier
PY  - 2007
SP  - 703
EP  - 718
VL  - 57
IS  - 3
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2273/
DO  - 10.5802/aif.2273
LA  - en
ID  - AIF_2007__57_3_703_0
ER  - 
%0 Journal Article
%A McNeal, Jeffery D.
%A Varolin, Dror
%T Analytic inversion of adjunction: $L^2$ extension theorems with gain
%J Annales de l'Institut Fourier
%D 2007
%P 703-718
%V 57
%N 3
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.2273/
%R 10.5802/aif.2273
%G en
%F AIF_2007__57_3_703_0
McNeal, Jeffery D.; Varolin, Dror. Analytic inversion of adjunction: $L^2$ extension theorems with gain. Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 703-718. doi : 10.5802/aif.2273. https://aif.centre-mersenne.org/articles/10.5802/aif.2273/

[1] Berndtsson, B. The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman, Ann. Inst. Fourier (Grenoble), Volume 46 (1996) no. 4, pp. 1083-1094 | DOI | EuDML | Numdam | MR | Zbl

[2] Demailly, J.-P. Multiplier ideal sheaves and analytic methods in algebraic geometry, ICTP Lect. Notes, Volume 6, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2001 School on Vanishing Theorems and Effective Results in Algebraic Geometry (Trieste, 2000) 1–148 | MR | Zbl

[3] Kollár, J. Singularities of pairs, Algebraic geometry – Santa Cruz (1995), pp. 221-287 (Proc. Sympos. Pure Math., 62, Part 1, Amer. Math. Soc., Providence, RI, 1997) | MR | Zbl

[4] Lazarsfeld, R. Positivity in algebraic geometry, I, II, Springer, 2004 | MR | Zbl

[5] McNeal, J. D. On large values of L 2 holomorphic functions, Math. Res. Let., Volume 3 (1996), pp. 247-259 | MR | Zbl

[6] Ohsawa, T. On the extension of L 2 holomorphic functions. III. Negligible weights, Math. Z., Volume 219 (1995) no. 2, pp. 215-225 | DOI | EuDML | MR | Zbl

[7] Ohsawa, T.; Takegoshi, K. On the extension of L 2 holomorphic functions, Math. Z., Volume 195 (1987) no. 2, pp. 197-204 | DOI | EuDML | MR | Zbl

[8] Siu, Y.-T. The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi, Geometric Complex Analysis, Hayama. World Scientific (1996), pp. 577-592 | MR | Zbl

[9] Siu, Y.-T. Invariance of plurigenera, Invent. Math., Volume 134 (1998) no. 3, p. 661-673. | DOI | MR | Zbl

[10] Siu, Y.-T. Extension of twisted pluricanonical sections with plurisubharmonic weight and invariance of semipositively twisted plurigenera for manifolds not necessarily of general type, Complex geometry, Springer-Verlag (2002), pp. 223-277 (Collection of papers dedicated to Hans Grauert) | MR | Zbl

Cité par Sources :