English

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 2j2j terms in the diagonal asymptotic expansion of the restriction to the (0,2j)(0,2j)-forms of the Bergman kernel associated to the spinc{}^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.

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}
}