Asymptotics of holomorphic sections of powers of a positive line bundle

Steve Zelditch[1]

  • [1] Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA

Séminaire Équations aux dérivées partielles (1997-1998)

  • Volume: 1997-1998, page 1-16

How to cite


Zelditch, Steve. "Asymptotics of holomorphic sections of powers of a positive line bundle." Séminaire Équations aux dérivées partielles 1997-1998 (1997-1998): 1-16. <>.

affiliation = {Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA},
author = {Zelditch, Steve},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-16},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Asymptotics of holomorphic sections of powers of a positive line bundle},
url = {},
volume = {1997-1998},
year = {1997-1998},

AU - Zelditch, Steve
TI - Asymptotics of holomorphic sections of powers of a positive line bundle
JO - Séminaire Équations aux dérivées partielles
PY - 1997-1998
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1997-1998
SP - 1
EP - 16
LA - eng
UR -
ER -


  1. J-M.Bismut and E.Vasserot, The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle, Comm.Math. Phys. 125 (1989), 355-367. Zbl0687.32023MR1016875
  2. P. Bleher and X. Di, Correlations between zeros of a random polynomial, J. Stat . Phys. 88 (1997), 269–305. Zbl0939.60047MR1468385
  3. E. Bogomolny, O. Bohigas, and P. Leboeuf, Quantum chaotic dynamics and random polynomials, J. Stat. Phys. 85 (1996), 639–679. Zbl0952.37506MR1418808
  4. T.Bouche, Convergence de la metrique de Fubini-Study d’un fibre lineaire positif, Annales de l’Institut Fourier (Grenoble) 40 (1990), 117- 130. Zbl0685.32015
  5. T.Bouche, Asymptotic results for hermitian line bundles over complex manifolds: the heat kernel approach, in Higher-dimensional Complex Varieties (Trento, 1994), 67-81, de Gruyter, Berlin (1996). Zbl0914.32010MR1463174
  6. L. Boutet de Monvel and V. Guillemin, The Spectral Theory of Toeplitz Operators, Ann. Math. Studies 99, Princeton Univ. Press, Princeton, 1981. Zbl0469.47021MR620794
  7. L.Boutet de Monvel and J.Sjostrand, Sur la singularite des noyaux de Bergman et de Szego, Asterisque 34-35 (1976), 123-164. Zbl0344.32010MR590106
  8. D.Catlin (to appear). 
  9. J.P.Demailly, Holomorphic Morse inequalities, in: Several Complex Variables and Complex Geometry, Part 2 (S.G.Krantz, ed.), AMS Proceedings of Symposia in Pure Math. 52 (1991), 93-114. Zbl0755.32008MR1128538
  10. H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Annalen 146 (1962), 331–368. Zbl0173.33004MR137127
  11. P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978. Zbl0408.14001MR507725
  12. J. H. Hannay, Chaotic analytic zero points: exact statistics for those of a random spin state, J. Phys. A: Math. Gen. 29 (1996), 101–105. Zbl0943.82505MR1383056
  13. L.Hormander, The Analysis of Linear Partial Differential Operators, Grund.Math.Wiss. 256, Springer-Verlag, N.Y. (1983). Zbl0521.35001
  14. S.Ji, Inequality for distortion function of invertible sheaves on Abelian varieties, Duke Math. J. 58 (1989), 657-667. Zbl0711.14024MR1016440
  15. G.Kempf, Metrics on invertible sheaves on Abelian varieties (1988). 
  16. M. Klimek, Pluripotential Theory, Clarendon Press, Oxford, 1991. Zbl0742.31001MR1150978
  17. P. Leboeuf and P. Shukla, Universal fluctuations of zeros of chaotic wavefunctions, J. Phys. A: Math. Gen.29 (1996), 4827-4835. Zbl0899.58058MR1418776
  18. P.Lelong and L.Gruman, Entire functions of several complex variables, Grund.Math.Wiss. 282, Springer-Verlag (1986). Zbl0583.32001MR837659
  19. J.Neuheisel and S.Zelditch, Zeros of completely integrable eigenfunctions on toric varieties (in preparation). 
  20. S. Nonnenmacher and A. Voros, Chaotic eigenfunctions in phase space, (preprint 1997). Zbl1079.81530MR1649013
  21. B.Shiffman and S.Zelditch, Distribution of zeros of random and of quantum chaotic sections of positive line bundles (preprint, 1998). Zbl0919.32020MR1675133
  22. A. I. Shnirelman, Ergodic properties of eigenfunctions, Usp. Mat. Nauk. 29/6 (1974), 181–182. Zbl0324.58020MR402834
  23. G. Tian, On a set of polarized Kähler metrics on algebraic manifolds, J. Diff. Geometry 32 (1990), 99–130. Zbl0706.53036MR1064867
  24. J.M.VanderKam, L norms and quantum ergodicity on the sphere, Int.Math.Res.Notices 7 (1997), 329-347. Zbl0877.58056MR1440572
  25. S. Zelditch, Szego kernels and a theorem of Tian, Int. Math. Res. Notices, to appear. Zbl0922.58082MR1616718
  26. S. Zelditch, A random matrix model for quantum mixing, Int. Math. Res. Notices 3 (1996), 115–137. Zbl0858.58048MR1383753
  27. S. Zelditch, Index and dynamics of quantized contact transformations, Annales de l’Institut Fourier (Grenoble) 47 (1997), 305–363. Zbl0865.47018

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