On Obtaining a Positive Line Bundle from the Weil-Petersson Class

In recent years, the near diagonal asymptotics of the equivariant components of the Szegö kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map.

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The asymptotics of the analytic torsion on CR manifolds with S1 action

Communications in Contemporary Mathematics ◽

10.1142/s0219199717500948 ◽

2019 ◽

Vol 21 (04) ◽

pp. 1750094 ◽

Cited By ~ 1

Author(s):

Chin-Yu Hsiao ◽

Rung-Tzung Huang

Keyword(s):

Line Bundle ◽

Asymptotic Formula ◽

Analytic Torsion ◽

Cr Manifold ◽

Cr Manifolds ◽

Dimension Formula ◽

Positive Line Bundle ◽

Positive Line

Let [Formula: see text] be a compact connected strongly pseudoconvex CR manifold of dimension [Formula: see text], [Formula: see text] with a transversal CR [Formula: see text]-action on [Formula: see text]. We introduce the Fourier components of the Ray–Singer analytic torsion on [Formula: see text] with respect to the [Formula: see text]-action. We establish an asymptotic formula for the Fourier components of the analytic torsion with respect to the [Formula: see text]-action. This generalizes the asymptotic formula of Bismut and Vasserot on the holomorphic Ray–Singer torsion associated with high powers of a positive line bundle to strongly pseudoconvex CR manifolds with a transversal CR [Formula: see text]-action.

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Käahler identity on Levi flat manifolds and application to the embedding

Nagoya Mathematical Journal ◽

10.1017/s0027763000007315 ◽

2000 ◽

Vol 158 ◽

pp. 87-93 ◽

Cited By ~ 7

Author(s):

Takeo Ohsawa ◽

Nessim Sibony

Keyword(s):

Line Bundle ◽

Finite Order ◽

Flat Manifold ◽

Positive Line Bundle ◽

Flat Manifolds ◽

Positive Line

AbstractIt is shown that any compact Levi flat manifold admitting a positive line bundle is embeddable into ℙn by a CR mapping with an arbitrarily high, though finite, order of regularity.

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ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748015000171 ◽

2015 ◽

Vol 16 (2) ◽

pp. 223-349 ◽

Cited By ~ 6

Author(s):

Jean-Michel Bismut ◽

Xiaonan Ma ◽

Weiping Zhang

Keyword(s):

Vector Bundle ◽

Line Bundle ◽

Differential Form ◽

Toeplitz Operators ◽

Vector Bundles ◽

Direct Image ◽

Analytic Torsion ◽

Leading Term ◽

Positive Line Bundle ◽

Positive Line

We use Toeplitz operators to evaluate the leading term in the asymptotics of the analytic torsion forms associated with a family of flat vector bundles $F_{p}$. For $p\in \mathbf{N}$, the flat vector bundle $F_{p}$ is the direct image of $L^{p}$, where $L$ is a holomorphic positive line bundle on the fibres of a flat fibration by compact Kähler manifolds. The leading term of the analytic torsion forms is the integral along the fibre of a locally defined differential form.

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Complex submanifolds, connections and asymptotics

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091508000539 ◽

2010 ◽

Vol 53 (2) ◽

pp. 373-383

Author(s):

Tatyana Foth

Keyword(s):

Line Bundle ◽

Complex Manifold ◽

Compact Complex Manifold ◽

Line Bundles ◽

Natural Connection ◽

Complex Submanifolds ◽

Positive Line Bundle ◽

Positive Line

AbstractLet L → X be a positive line bundle on a compact complex manifold X. For compact submanifolds Y, S of X and a holomorphic submersion Y → S with compact fibre, we study curvature of a natural connection on certain line bundles on S.

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