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The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle. (English) Zbl 0687.32023

Let M be a compact complex manifold equipped with a smooth hermitian metric, \(\zeta\) a holomorphic hermitian vector bundle, \(\mu\) a positive hermitian line bundle. Let \(e_ p\), \(p\in {\mathbb{N}}\), be a holomorphic hermitian flat vector bundle. Assume \(\mu\) is equipped with a metric whose curvature is positive and let \(\tau_ p\) be the Ray-Singer analytic torsion of the Dolbeault complex on \(\mu^{\otimes p}\otimes \zeta \otimes E_ p\) [D. B. Ray and I. M. Singer, Ann. Math., II. Ser. 98, 154-177 (1973; Zbl 0267.32014).
In the paper the authors establish an asymptotic formula for Log \(\tau_ p\) as \(p\to +\infty\).
Reviewer: G.Tomassini

MSC:

32L05 Holomorphic bundles and generalizations
32Q99 Complex manifolds
58A10 Differential forms in global analysis

Citations:

Zbl 0267.32014
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References:

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