Analytic inversion of adjunction: L 2 extension theorems with gain
Annales de l'Institut Fourier, Volume 57 (2007) no. 3, p. 703-718

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.

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.

DOI : https://doi.org/10.5802/aif.2273
Classification:  32A99,  32Q99
Keywords: Ohsawa-Takegoshi-type extension, twisted Bochner-Kodaira technique, denominators
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {3},
     year = {2007},
     pages = {703-718},
     doi = {10.5802/aif.2273},
     mrnumber = {2336826},
     zbl = {pre05176602},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 57 (2007) no. 3, pp. 703-718. doi : 10.5802/aif.2273. http://www.numdam.org/item/AIF_2007__57_3_703_0/

[1] Berndtsson, B. The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman, Ann. Inst. Fourier (Grenoble), Tome 46 (1996) no. 4, pp. 1083-1094 | Article | Numdam | MR 1415958 | Zbl 0853.32024

[2] Demailly, J.-P. Multiplier ideal sheaves and analytic methods in algebraic geometry, ICTP Lect. Notes, Abdus Salam Int. Cent. Theoret. Phys., Trieste, Tome 6 (2001) (School on Vanishing Theorems and Effective Results in Algebraic Geometry (Trieste, 2000) 1–148) | MR 1919457 | Zbl 1102.14300 | Zbl 01816813

[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 1492525 | Zbl 0905.14002

[4] Lazarsfeld, R. Positivity in algebraic geometry, I, II, Springer (2004) | MR 2095471 | Zbl 1093.14500 | Zbl 1066.14021

[5] Mcneal, J. D. On large values of L 2 holomorphic functions, Math. Res. Let., Tome 3 (1996), pp. 247-259 | MR 1386844 | Zbl 0865.32009

[6] Ohsawa, T. On the extension of L 2 holomorphic functions. III. Negligible weights, Math. Z., Tome 219 (1995) no. 2, pp. 215-225 | Article | MR 1337216 | Zbl 0823.32006

[7] Ohsawa, T.; Takegoshi, K. On the extension of L 2 holomorphic functions, Math. Z., Tome 195 (1987) no. 2, pp. 197-204 | Article | MR 892051 | Zbl 0625.32011

[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 1453639 | Zbl 0941.32021

[9] Siu, Y.-T. Invariance of plurigenera, Invent. Math., Tome 134 (1998) no. 3, p. 661-673. | Article | MR 1660941 | Zbl 0955.32017

[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 1922108 | Zbl 1007.32010