Superconnection and family Bergman kernels

DOI10.1016/j.crma.2006.11.013zbMath1109.32002arXivmath/0607404OpenAlexW2085741218MaRDI QIDQ866585

Xiaonan Ma, Weiping Zhang

Publication date: 14 February 2007

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607404

Mathematics Subject Classification ID

Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (14)

Superconnection and family Bergman kernels ⋮ Geometric quantization of Hamiltonian flows and the Gutzwiller trace formula ⋮ Quantization of symplectic fibrations and canonical metrics ⋮ Complex geometry and dynamical systems. Abstracts from the workshop held September 4--10, 2022 ⋮ The asymptotics of the holomorphic torsion forms ⋮ The asymptotics of the holomorphic analytic torsion forms ⋮ Toeplitz operators and the full asymptotic torsion forms ⋮ ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS ⋮ The asymptotic of curvature of direct image bundle associated with higher powers of a relatively ample line bundle ⋮ Superconnection and family Bergman kernels ⋮ Positivity and vanishing theorems for ample vector bundles ⋮ A remark on characterizations of Griffiths positivity through asymptotic conditions ⋮ Geometric quantization of symplectic maps and Witten's asymptotic conjecture ⋮ Second variation of Selberg zeta functions and curvature asymptotics

Cites Work

• Unnamed Item
• Unnamed Item
• The spin\(^{\mathbf c}\) Dirac operator on high tensor powers of a line bundle
• Superconnection and family Bergman kernels
• The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
• Some symplectic geometry on compact Kähler manifolds. I
• Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion. II: Direct images and Bott-Chern forms. III: Quillen metrics on holomorphic determinants
• The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle
• Holomorphic Morse inequalities and Bergman kernels
• Complex Monge-Ampere and Symplectic Manifolds
• Generalized Bergman kernels on symplectic manifolds
• On the asymptotic expansion of Bergman kernel

This page was built for publication: Superconnection and family Bergman kernels