Automorphisms of OT manifolds and ray class numbers

TL;DR

This paper computes the automorphism group of OT manifolds of simple type and relates their structure to ray class groups, advancing understanding of the connection between geometry and number theory.

Contribution

It provides a detailed computation of the automorphism group and links graded pieces to ray class groups, offering new insights into the geometric interpretation of class numbers.

Findings

Automorphism group of OT manifolds of simple type is explicitly computed.

Graded pieces under a natural filtration relate to ray class groups.

Progress made towards understanding the geometric reflection of class numbers.

Abstract

We compute the automorphism group of OT manifolds of simple type. We show that the graded pieces under a natural filtration are related to a certain ray class group of the underlying number field. This does not solve the open question whether the geometry of the OT manifold sees the class number directly, but brings us a lot closer to a possible solution.