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

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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

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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

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  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
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  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

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