The first terms in the expansion of the Bergman kernel in higher degrees

DOI10.2140/PJM.2015.274.373zbMATH Open1320.32025arXiv1210.1717OpenAlexW2017905095MaRDI QIDQ2346680

Martin Puchol, Jia-Lin Zhu

Publication date: 3 June 2015

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Abstract: We establish the cancellation of the first $2j$ terms in the diagonal asymptotic expansion of the restriction to the $(0,2j)$-forms of the Bergman kernel associated to the spin${}^c$ Dirac operator on high tensor powers of a positive line bundle twisted by a (non necessarily holomorphic) complex vector bundle, over a compact K"{a}hler manifold. Moreover, we give a local formula for the first and the second (non-zero) leading coefficients.

Full work available at URL: https://arxiv.org/abs/1210.1717

zbMATH Keywords

asymptotic expansionBergman kernelquantization

Mathematics Subject Classification ID

Geometric quantization (53D50) Compact Kähler manifolds: generalizations, classification (32J27) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (3)

Unnamed Item ⋮ Szegő kernel, regular quantizations and spherical CR-structures ⋮ Unnamed Item

This page was built for publication: The first terms in the expansion of the Bergman kernel in higher degrees