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

Abstract

top
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.

How to cite

top

McNeal, 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
  1. B. Berndtsson, The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman, Ann. Inst. Fourier (Grenoble) 46 (1996), 1083-1094 Zbl0853.32024MR1415958
  2. 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
  3. J. Kollár, Singularities of pairs, Algebraic geometry – Santa Cruz (1995), 221-287 Zbl0905.14002MR1492525
  4. R. Lazarsfeld, Positivity in algebraic geometry, I, II, Springer (2004) Zbl1066.14021MR2095471
  5. J. D. McNeal, On large values of L 2 holomorphic functions, Math. Res. Let. 3 (1996), 247-259 Zbl0865.32009MR1386844
  6. T. Ohsawa, On the extension of L 2 holomorphic functions. III. Negligible weights, Math. Z. 219 (1995), 215-225 Zbl0823.32006MR1337216
  7. T. Ohsawa, K. Takegoshi, On the extension of L 2 holomorphic functions, Math. Z. 195 (1987), 197-204 Zbl0625.32011MR892051
  8. Y.-T. Siu, The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi, Geometric Complex Analysis, Hayama. World Scientific (1996), 577-592 Zbl0941.32021MR1453639
  9. Y.-T. Siu, Invariance of plurigenera, Invent. Math. 134 (1998), 661-673. Zbl0955.32017MR1660941
  10. 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

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.