Asymptotics of holomorphic sections of powers of a positive line bundle
- [1] Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA
Séminaire Équations aux dérivées partielles (1997-1998)
- Volume: 1997-1998, page 1-16
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top- 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
- P. Bleher and X. Di, Correlations between zeros of a random polynomial, J. Stat . Phys. 88 (1997), 269–305. Zbl0939.60047MR1468385
- E. Bogomolny, O. Bohigas, and P. Leboeuf, Quantum chaotic dynamics and random polynomials, J. Stat. Phys. 85 (1996), 639–679. Zbl0952.37506MR1418808
- 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
- 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
- L. Boutet de Monvel and V. Guillemin, The Spectral Theory of Toeplitz Operators, Ann. Math. Studies 99, Princeton Univ. Press, Princeton, 1981. Zbl0469.47021MR620794
- 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
- D.Catlin (to appear).
- 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
- H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Annalen 146 (1962), 331–368. Zbl0173.33004MR137127
- P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978. Zbl0408.14001MR507725
- 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
- L.Hormander, The Analysis of Linear Partial Differential Operators, Grund.Math.Wiss. 256, Springer-Verlag, N.Y. (1983). Zbl0521.35001
- S.Ji, Inequality for distortion function of invertible sheaves on Abelian varieties, Duke Math. J. 58 (1989), 657-667. Zbl0711.14024MR1016440
- G.Kempf, Metrics on invertible sheaves on Abelian varieties (1988).
- M. Klimek, Pluripotential Theory, Clarendon Press, Oxford, 1991. Zbl0742.31001MR1150978
- P. Leboeuf and P. Shukla, Universal fluctuations of zeros of chaotic wavefunctions, J. Phys. A: Math. Gen.29 (1996), 4827-4835. Zbl0899.58058MR1418776
- P.Lelong and L.Gruman, Entire functions of several complex variables, Grund.Math.Wiss. 282, Springer-Verlag (1986). Zbl0583.32001MR837659
- J.Neuheisel and S.Zelditch, Zeros of completely integrable eigenfunctions on toric varieties (in preparation).
- S. Nonnenmacher and A. Voros, Chaotic eigenfunctions in phase space, (preprint 1997). Zbl1079.81530MR1649013
- B.Shiffman and S.Zelditch, Distribution of zeros of random and of quantum chaotic sections of positive line bundles (preprint, 1998). Zbl0919.32020MR1675133
- A. I. Shnirelman, Ergodic properties of eigenfunctions, Usp. Mat. Nauk. 29/6 (1974), 181–182. Zbl0324.58020MR402834
- G. Tian, On a set of polarized Kähler metrics on algebraic manifolds, J. Diff. Geometry 32 (1990), 99–130. Zbl0706.53036MR1064867
- J.M.VanderKam, norms and quantum ergodicity on the sphere, Int.Math.Res.Notices 7 (1997), 329-347. Zbl0877.58056MR1440572
- S. Zelditch, Szego kernels and a theorem of Tian, Int. Math. Res. Notices, to appear. Zbl0922.58082MR1616718
- S. Zelditch, A random matrix model for quantum mixing, Int. Math. Res. Notices 3 (1996), 115–137. Zbl0858.58048MR1383753
- S. Zelditch, Index and dynamics of quantized contact transformations, Annales de l’Institut Fourier (Grenoble) 47 (1997), 305–363. Zbl0865.47018