# Analytic inversion of adjunction: ${L}^{2}$ extension theorems with gain

Jeffery D. McNeal^{[1]}; Dror Varolin^{[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)

Annales de l’institut Fourier (2007)

- Volume: 57, Issue: 3, page 703-718
- ISSN: 0373-0956

## Access Full Article

top## Abstract

top## How to cite

topMcNeal, Jeffery D., and Varolin, Dror. "Analytic inversion of adjunction: $L^2$ extension theorems with gain." Annales de l’institut Fourier 57.3 (2007): 703-718. <http://eudml.org/doc/10238>.

@article{McNeal2007,

abstract = {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.},

affiliation = {Department of Mathematics 100 mathematics building 231 W. 18th avenue Columbus, Ohio 43210-1174 (USA); Stony Brook University Department of Mathematics Stony Brook NY 11794-3651 (USA)},

author = {McNeal, Jeffery D., Varolin, Dror},

journal = {Annales de l’institut Fourier},

keywords = {Ohsawa-Takegoshi-type extension; twisted Bochner-Kodaira technique; denominators},

language = {eng},

number = {3},

pages = {703-718},

publisher = {Association des Annales de l’institut Fourier},

title = {Analytic inversion of adjunction: $L^2$ extension theorems with gain},

url = {http://eudml.org/doc/10238},

volume = {57},

year = {2007},

}

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

PB - Association des Annales de l’institut Fourier

VL - 57

IS - 3

SP - 703

EP - 718

AB - 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.

LA - eng

KW - Ohsawa-Takegoshi-type extension; twisted Bochner-Kodaira technique; denominators

UR - http://eudml.org/doc/10238

ER -

## References

top- B. Berndtsson, The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman, Ann. Inst. Fourier (Grenoble) 46 (1996), 1083-1094 Zbl0853.32024MR1415958
- J.-P. Demailly, Multiplier ideal sheaves and analytic methods in algebraic geometry, ICTP Lect. Notes 6 (2001), Abdus Salam Int. Cent. Theoret. Phys., Trieste Zbl1102.14300MR1919457
- J. Kollár, Singularities of pairs, Algebraic geometry – Santa Cruz (1995), 221-287 Zbl0905.14002MR1492525
- R. Lazarsfeld, Positivity in algebraic geometry, I, II, Springer (2004) Zbl1066.14021MR2095471
- J. D. McNeal, On large values of ${L}^{2}$ holomorphic functions, Math. Res. Let. 3 (1996), 247-259 Zbl0865.32009MR1386844
- T. Ohsawa, On the extension of ${L}^{2}$ holomorphic functions. III. Negligible weights, Math. Z. 219 (1995), 215-225 Zbl0823.32006MR1337216
- T. Ohsawa, K. Takegoshi, On the extension of ${L}^{2}$ holomorphic functions, Math. Z. 195 (1987), 197-204 Zbl0625.32011MR892051
- Y.-T. Siu, The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi, Geometric Complex Analysis, Hayama. World Scientific (1996), 577-592 Zbl0941.32021MR1453639
- Y.-T. Siu, Invariance of plurigenera, Invent. Math. 134 (1998), 661-673. Zbl0955.32017MR1660941
- Y.-T. Siu, 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), 223-277 Zbl1007.32010MR1922108

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.