The Analogue of Dedekind Eta Functions for Calabi-Yau Manifilolds II. (Algebraic, Analytic Discriminants and the Analogue of Baily-Borel Compactification of the Moduli Space of CY Manifolds.)

TL;DR

This paper constructs an analogue of Dedekind eta-functions for Calabi-Yau manifolds, linking it to Laplacian determinants and developing a compactification of the moduli space with properties similar to Baily-Borel.

Contribution

It introduces a new eta-function analogue for CY moduli spaces and establishes its relation to Laplacian determinants and a minimal compactification.

Findings

L-two norm of eta equals regularized Laplacian determinant

Constructed a Baily-Borel type compactification for CY moduli

Proved the compactification is minimal

Abstract

In this paper we construct the analogue of Dedekind eta-function on the moduli space of polarized CY manifolds. We prove that the L-two norm of eta is the regularized determinants of the Laplacians of the CY metric on (0,1) forms. We construct the analogue of the Baily-Borel Compactification of the moduli space of polarized CY and prove that it has the same properties as the Baily-Borel compactification of the locally symmetric Hermitian spaces. We proved that the compactification constructed in the paper is the minimal.