arXiv subjects

Kai Köhler

Publications and source records attributed to Kai Köhler.

2 recordsLinked to original sources

arXiv2026

Asymptotics of holomorphic torsion on orbifolds and an equivariant arithmetic Hilbert-Samuel theorem

We compute the $\log p$-part of the asymptotic expansion of the holomorphic torsion of the $p$-th power of a positive line bundle in terms of characteristic classes. This is done for orbifold and equivariant torsions. In the equivariant case the exponents in the expansion are less than or equal to the dimension of the fixed point set. We deduce a corresponding equivariant arithmetic Hilbert-Samuel theorem in Arakelov geometry.

math.DG↗

arXiv2026

The full asymptotic expansion of analytic torsion on homogeneous spaces

The full asymptotic expansion of the equivariant complex Ray-Singer torsion for high powers of line bundles on symmetric spaces is given in an explicit form. In the case of isolated fixed points this expansion is given for general complex homogeneous spaces. Furthermore the full asymptotic expansion is given for the complex analytic torsion form associated to fibrations by projective curves. The expansions are compared with results by Bismut-Vasserot, Finski and Puchol. The results are applied to lattice representations of Chevalley groups.

math.DG↗