The analytic torsions of the line bundles over the quadrics

概要

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The analytic torsions of the line bundles over the quadrics are computed directly from the defining spectral zeta functions associated with the Dolbeault complex. The spectral data needed are calculated using the branching rule for the symmetric pair (SO(n+2), SO(2)×SO(n)) given by the author in [2]. The spectral zeta functions for the analytic torsions are shown to be of the form treated by the author in [3] and the derivatives at $0$ are computed by the method developed there. The result is compared with the well-known Kai Köhler's paper [1]. The cancellation of the spectral zeta functions is observed, on the level of the spectral data.
2010-11-12