Generic analytic polyhedron with non-compact automorphism group

TL;DR

This paper proves a rigidity theorem characterizing generic analytic polyhedra with non-compact automorphism groups as products of a complex manifold and a polydisk, with explicit descriptions based on automorphism group limit sets.

Contribution

It establishes a new classification theorem for analytic polyhedra with non-compact automorphism groups, linking geometric structure to automorphism group dynamics.

Findings

Polyhedra with non-compact automorphism groups are biholomorphic to a product involving a polydisk.

The complex manifold component and polydisk dimension are explicitly described via automorphism group limit sets.

The theorem provides a structural insight into the automorphism groups of analytic polyhedra.

Abstract

In this paper we prove the following rigidity theorem: a generic analytic polyhedron with non-compact automorphism group is biholomorphic to the product of a complex manifold with compact automorphism group and a polydisk. Moreover, this complex manifold and the dimension of this polydisk can be explicitly described in terms of the limit set of the automorphism group.