The spin $^{\bf c}$ Dirac operator on high tensor powers of a line bundle

By Xiaonan Ma, G. Marinescu. 2001

69 citations recorded by the source corpus.

Abstract. We study the asymptotic of the spectrum of the ${\rm spin^c}$ Dirac operator on high tensor powers of a line bundle. As application, we get a simple proof of the main result of Guillemin–Uribe [13, Theorem 2], which was originally proved by using the analysis of Toeplitz operators of Boutet de Monvel and Guillemin [10].

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d57219ffd6d5701d5e0c6b9cf3f2d6e8c773a817

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the asymptotic expansion of Bergman kernel (2004, background): “In Section 2, we recall a result on the spectral gap of the spin Dirac operator [25].”
Generalized Bergman kernels on symplectic manifolds (2004, methodology): “The asymptotic of the spectrum of the renormalized Bochner– Laplacian on L when p → ∞ is studied in various generalities in [9, 15, 24] by applying the analysis of Toeplitz structures of Boutet de Monvel–Guillemin [13], and in [27] as a direct application of Lichnerowicz formula.”