The analogue of the Dedekind eta function for CY manifolds I
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Jamey Bass
Abstract
This is the first of series of articles in which we are going to study the regularized determinants of the Laplacians of Calabi-Yau metrics acting on (0, q) forms on the moduli space of CY manifolds with a fixed polarization.
It is well known that in the case of elliptic curves, the Kronecker limit formula gives an explicit formula for the regularized determinant of the flat metric with fixed volume on the elliptic curves. The following formula holds in this case:
where η(τ) is the Dedekind eta function. It is well known fact that η(τ)24 is a cusp automorphic form of weight 12 related to the discriminant of the elliptic curve.
Formula (1) implies that there exists a holomorphic section of some power of the line bundle of the classes of cohomologies of (1, 0) forms of the elliptic curves over the moduli space with an L2 norm equal to det Δ(0, 1) (τ). This section is η(τ)24. The purpose of this project is to find the relations between the regularized determinants of CY metric on (0, 1) forms and algebraic discriminants of CY manifolds.
In this paper we will establish the local analogue of the formula (1) for CY manifolds.
© Walter de Gruyter
Articles in the same Issue
- Mappings of finite distortion: Capacity and modulus inequalities
- Khintchine type inequalities for reduced free products and applications
- The analogue of the Dedekind eta function for CY manifolds I
- On deformations of ℚ-factorial symplectic varieties
- Uniformization of Deligne-Mumford curves
- A T1 theorem for integral transformations with operator-valued kernel
- Rank and matrix coefficients for simply laced groups
- A K-theoretic proof of Boutet de Monvel's index theorem for boundary value problems
Articles in the same Issue
- Mappings of finite distortion: Capacity and modulus inequalities
- Khintchine type inequalities for reduced free products and applications
- The analogue of the Dedekind eta function for CY manifolds I
- On deformations of ℚ-factorial symplectic varieties
- Uniformization of Deligne-Mumford curves
- A T1 theorem for integral transformations with operator-valued kernel
- Rank and matrix coefficients for simply laced groups
- A K-theoretic proof of Boutet de Monvel's index theorem for boundary value problems
