The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle
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 \(\mu^{\otimes p}\otimes \zeta \otimes E_ p\) [\textit{D. B. Ray} and \textit{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 \(p\to +\infty\).
scientific article; zbMATH DE number 4125795