Weil-Petersson volumes of the moduli spaces of CY manifolds

@article{Todorov2004WeilPeterssonVO,
  title={Weil-Petersson volumes of the moduli spaces of CY manifolds},
  author={Andrey N. Todorov},
  journal={Communications in Analysis and Geometry},
  year={2004},
  volume={15},
  pages={381-405}
}
  • A. Todorov
  • Published 4 August 2004
  • Mathematics
  • Communications in Analysis and Geometry
In this paper it is proved that the volumes of the moduli spaces of polarized CY manifolds with respect to the Weil-Petersson metrics are finite and they are rational numbers. 

On the Weil-Petersson Volume and the First Chern Class of the Moduli Space of Calabi-Yau Manifolds

In this paper, we proved that the Weil-Petersson volume of Calabi-Yau moduli is a rational number. We also proved that the integrations of the invariants of the Ricci curvature of the Weli-Petersson

Remarks on the Chern classes of Calabi-Yau moduli

We prove that the first Chern form of the moduli space of polarized Calabi-Yau manifolds, with the Hodge metric or the Weil-Petersson metric, represent the first Chern class of the canonical

Finiteness of volume of moduli spaces

We give a ``physics proof'' of a conjecture made by the first author at Strings 2005, that the moduli spaces of certain conformal field theories are finite volume in the Zamolodchikov metric, using

CALABI-YAU MANIFOLDS WHOSE MODULI SPACES ARE LOCALLY SYMMETRIC MANIFOLDS AND NO QUANTUM CORRECTIONS

It is observed that there are a natural sequence of CY manifolds Mg that are double covers of CP ramified over 2g + 2 hyperplanes and some of them are obtained from the Jacobian J(Cg) of

Gauss–Bonnet–Chern theorem on moduli space

In this paper, we prove a Gauss–Bonnet–Chern type theorem in full generality for the Chern–Weil forms of Hodge bundles. That is, the Chern–Weil forms compute the corresponding Chern classes. This

Gauss–Bonnet–Chern theorem on moduli space

In this paper, we prove a Gauss–Bonnet–Chern type theorem in full generality for the Chern–Weil forms of Hodge bundles. That is, the Chern–Weil forms compute the corresponding Chern classes. This

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.)

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

Distribution of flux vacua around singular points in Calabi-Yau moduli space

We study the distribution of type-IIB flux vacua in the moduli space near various singular loci, e.g. conifolds, ADE singularities on P1, Argyres-Douglas point etc, using the Ashok-Douglas density

Compactness and Non-compactness for the Yamabe Problem on Manifolds With Boundary

We study the problem of conformal deformation of Riemannian structure to constant scalar curvature with zero mean curvature on the boundary. We prove compactness for the full set of solutions when

A global Torelli theorem for hyperkahler manifolds

A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. We compute a mapping class group of a hypekahler manifold $M$, showing that it is

References

SHOWING 1-10 OF 17 REFERENCES

The Weil-Petersson geometry of the moduli space ofSU(n≧3) (Calabi-Yau) manifolds I

The Weil-Petersson metric is defined on the moduli space of Calabi-Yau manifolds. The curvature of this Weil-Petersson metrics is computed and its potential is explicitely defined. It is proved that

Finiteness of volume of moduli spaces

We give a ``physics proof'' of a conjecture made by the first author at Strings 2005, that the moduli spaces of certain conformal field theories are finite volume in the Zamolodchikov metric, using

WEIL–PETERSSON GEOMETRY ON MODULI SPACE OF POLARIZED CALABI–YAU MANIFOLDS

In this paper, we define and study the Weil–Petersson geometry. Under the framework of the Weil–Petersson geometry, we study the Weil–Petersson metric and the Hodge metric. Among the other results,

On the curvature tensor of the Hodge metric of moduli space of polarized Calabi-Yau threefolds

In this article, we give an expression and some estimates of the curvature tensor of the Hodge metric over the moduli space of a polarized calabi-Yau threefold. The symmetricity of the Yukawa

Generalized Hodge metrics and BCOV torsion on Calabi-Yau moduli

Abstract We establish an unexpected relation among the Weil-Petersson metric, the generalized Hodge metrics and the BCOV torsion. Using this relation, we prove that certain kind of moduli spaces of

Quasi-projective moduli for polarized manifolds

  • E. Viehweg
  • Mathematics
    Ergebnisse der Mathematik und ihrer Grenzgebiete
  • 1995
This text discusses two subjects of quite different natures: construction methods for quotients of quasi-projective schemes either by group actions or by equivalence relations; and properties of

Curvature of the Weil-Petersson Metric in the Moduli Space of Compact Kähler-Einstein Manifolds of Negative First Chem Class

For compact Riemann surfaces of genus at least two, using Petersson’s Hermitian pairing for automorphic forms, Weil introduced a Hermitian metric for the Teiclmuller space, now known as the

Shafarevich's Conjecture for CY Manifolds I

In this paper we first study the moduli spaces related to Calabi-Yau manifolds. We then apply the results to the following problem. Let $C$ be a fixed Riemann surface with fixed finite number of

Chaotic coupling constants

Complex Manifolds

is holomorphic. Thus P has the structure of a complex manifold, called complex projective space. The “coordinates” Z + [Z0, . . . , Zn] are called homogeneous coordinates on P. P is compact, since we