The first terms in the expansion of the Bergman kernel in higher degrees
Differential Geometry
2017-01-04 v2
Abstract
We establish the cancellation of the first terms in the diagonal asymptotic expansion of the restriction to the -forms of the Bergman kernel associated to the spin 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.
Keywords
Cite
@article{arxiv.1210.1717,
title = {The first terms in the expansion of the Bergman kernel in higher degrees},
author = {Martin Puchol and Jialin Zhu},
journal= {arXiv preprint arXiv:1210.1717},
year = {2017}
}