Remark on the Off-Diagonal Expansion of the Bergman Kernel on Compact Kähler Manifolds

Xiaonan Ma , George Marinescu

Communications in Mathematics and Statistics ›› 2013, Vol. 1 ›› Issue (1) : 37 -41.

PDF
Communications in Mathematics and Statistics ›› 2013, Vol. 1 ›› Issue (1) : 37 -41. DOI: 10.1007/s40304-013-0004-8
Original Article

Remark on the Off-Diagonal Expansion of the Bergman Kernel on Compact Kähler Manifolds

Author information +
History +
PDF

Abstract

In this short note, we compare our previous work on the off-diagonal expansion of the Bergman kernel and the preprint of Lu–Shiffman (arXiv:1301.2166). In particular, we note that the vanishing of the coefficient of p −1/2 is implicitly contained in Dai–Liu–Ma’s work (J. Differ. Geom. 72(1), 1–41, 2006) and was explicitly stated in our book (Holomorphic Morse inequalities and Bergman kernels. Progress in Math., vol. 254, 2007).

Keywords

Kähler manifold / Bergman kernel of a positive line bundle

Cite this article

Download citation ▾
Xiaonan Ma, George Marinescu. Remark on the Off-Diagonal Expansion of the Bergman Kernel on Compact Kähler Manifolds. Communications in Mathematics and Statistics, 2013, 1(1): 37-41 DOI:10.1007/s40304-013-0004-8

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Boutet de Monvel L., Sjöstrand J. Sur la singularité des noyaux de Bergman et de Szegö. Journées Équations aux Dérivées Partielles de Rennes (1975). 1976 Paris: Soc. Math. France. 123-164

[2]

Dai X., Liu K., Ma X. On the asymptotic expansion of Bergman kernel. J. Differ. Geom.. 2006, 72 1 1-41

[3]

Lu, Z., Shiffman, B.: Asymptotic expansion of the off-diagonal Bergman kernel on compact Kähler manifolds. Preprint arXiv:1301.2166

[4]

Ma X., Marinescu G. Holomorphic Morse Inequalities and Bergman Kernels. 2007 Basel: Birkhäuser

[5]

Ma X., Marinescu G. Berezin-Toeplitz quantization on Kähler manifolds. J. Reine Angew. Math.. 2012, 662 1-56

[6]

Shiffman B., Zelditch S. Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds. J. Reine Angew. Math.. 2002, 544 181-222

AI Summary AI Mindmap
PDF

134

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/