Asymptotics of holomorphic sections of powers of a positive line bundle
Zelditch, Steve1
1 Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1997-1998), Exposé no. 22, 16 p.
Zelditch, Steve 1

1 Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA 
@article{SEDP_1997-1998____A22_0,
     author = {Zelditch, Steve},
     title = {Asymptotics of holomorphic sections of powers of a positive line bundle},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:22},
     pages = {1--16},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {1997-1998},
     zbl = {1057.32501},
     mrnumber = {1660535},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_1997-1998____A22_0/}
}
TY  - JOUR
AU  - Zelditch, Steve
TI  - Asymptotics of holomorphic sections of powers of a positive line bundle
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:22
PY  - 1997-1998
SP  - 1
EP  - 16
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/item/SEDP_1997-1998____A22_0/
LA  - en
ID  - SEDP_1997-1998____A22_0
ER  - 
%0 Journal Article
%A Zelditch, Steve
%T Asymptotics of holomorphic sections of powers of a positive line bundle
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:22
%D 1997-1998
%P 1-16
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://www.numdam.org/item/SEDP_1997-1998____A22_0/
%G en
%F SEDP_1997-1998____A22_0
Zelditch, Steve. Asymptotics of holomorphic sections of powers of a positive line bundle. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1997-1998), Exposé no. 22, 16 p. http://www.numdam.org/item/SEDP_1997-1998____A22_0/

[Bis.V] 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. | MR | Zbl

[BlD] P. Bleher and X. Di, Correlations between zeros of a random polynomial, J. Stat . Phys. 88 (1997), 269–305. | MR | Zbl

[BBL] E. Bogomolny, O. Bohigas, and P. Leboeuf, Quantum chaotic dynamics and random polynomials, J. Stat. Phys. 85 (1996), 639–679. | MR | Zbl

[Bou.1] T.Bouche, Convergence de la metrique de Fubini-Study d’un fibre lineaire positif, Annales de l’Institut Fourier (Grenoble) 40 (1990), 117- 130. | Numdam | Zbl

[Bou.2] 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). | MR | Zbl

[BG] L. Boutet de Monvel and V. Guillemin, The Spectral Theory of Toeplitz Operators, Ann. Math. Studies 99, Princeton Univ. Press, Princeton, 1981. | MR | Zbl

[BS] L.Boutet de Monvel and J.Sjostrand, Sur la singularite des noyaux de Bergman et de Szego, Asterisque 34-35 (1976), 123-164. | Numdam | MR | Zbl

[C] D.Catlin (to appear).

[D] 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. | MR | Zbl

[Gr] H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Annalen 146 (1962), 331–368. | MR | Zbl

[GH] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978. | MR | Zbl

[Ha] 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. | MR | Zbl

[Ho I] L.Hormander, The Analysis of Linear Partial Differential Operators, Grund.Math.Wiss. 256, Springer-Verlag, N.Y. (1983). | Zbl

[Ji] S.Ji, Inequality for distortion function of invertible sheaves on Abelian varieties, Duke Math. J. 58 (1989), 657-667. | MR | Zbl

[K] G.Kempf, Metrics on invertible sheaves on Abelian varieties (1988).

[Kl] M. Klimek, Pluripotential Theory, Clarendon Press, Oxford, 1991. | MR | Zbl

[LS] P. Leboeuf and P. Shukla, Universal fluctuations of zeros of chaotic wavefunctions, J. Phys. A: Math. Gen.29 (1996), 4827-4835. | MR | Zbl

[LG] P.Lelong and L.Gruman, Entire functions of several complex variables, Grund.Math.Wiss. 282, Springer-Verlag (1986). | MR | Zbl

[NZ] J.Neuheisel and S.Zelditch, Zeros of completely integrable eigenfunctions on toric varieties (in preparation).

[NV] S. Nonnenmacher and A. Voros, Chaotic eigenfunctions in phase space, (preprint 1997). | MR | Zbl

[Sh.Z] B.Shiffman and S.Zelditch, Distribution of zeros of random and of quantum chaotic sections of positive line bundles (preprint, 1998). | MR

[Shn1] A. I. Shnirelman, Ergodic properties of eigenfunctions, Usp. Mat. Nauk. 29/6 (1974), 181–182. | MR

[T] G. Tian, On a set of polarized Kähler metrics on algebraic manifolds, J. Diff. Geometry 32 (1990), 99–130. | MR | Zbl

[V] J.M.VanderKam, L ∞ norms and quantum ergodicity on the sphere, Int.Math.Res.Notices 7 (1997), 329-347. | MR | Zbl

[Z1] S. Zelditch, Szego kernels and a theorem of Tian, Int. Math. Res. Notices, to appear. | MR | Zbl

[Z2] S. Zelditch, A random matrix model for quantum mixing, Int. Math. Res. Notices 3 (1996), 115–137. | MR | Zbl

[Z3] S. Zelditch, Index and dynamics of quantized contact transformations, Annales de l’Institut Fourier (Grenoble) 47 (1997), 305–363. | Numdam | Zbl