The asymptotic of curvature of direct image bundle associated with higher powers of a relatively ample line bundle
Journal article, 2021

Let π: X→ M be a holomorphic fibration with compact fibers and L a relatively ample line bundle over X. We obtain the asymptotic of the curvature of L -metric and Qullien metric on the direct image bundle π (L ⊗ K ) up to the lower order terms than k , for large k. As an application we prove that the analytic torsion τ (∂¯) satisfies ∂∂¯log(τk(∂¯))2=o(kn-1), where n is the dimension of fibers.

L -metric 2

Asymptotics

Curvature

Quillen metric

Holomorphic fibration

Author

Xueyuan Wan

Chongqing University of Technology

Genkai Zhang

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Geometriae Dedicata

0046-5755 (ISSN) 1572-9168 (eISSN)

Vol. In Press

Subject Categories

Geometry

Discrete Mathematics

Mathematical Analysis

DOI

10.1007/s10711-021-00625-y

More information

Latest update

6/3/2021 1