Questions tagged [weil-petersson-metric]
The Weil-Petersson metric is a Kahler metric on the moduli space of Calabi-Yau varieties, the moduli space of general type varieties, the moduli space of K-stable Fano varieties, and more generally, we can define it on the moduli space of stable varieties.
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Goldman symplectic form vs Weil–Petersson symplectic form
I'm confused about the exact multiplicative factor that relates Goldman symplectic form on the $\operatorname{SL}(2,\mathbb R)$-character variety and the Weil–Petersson symplectic form on Teichmüller ...
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Integration à la Mirzakhani
Let $$
\gamma = \sum_i c_i \gamma_i
$$
be a multi-curve on a hyperbolic surface $S$. For any $f: \mathbb{R}^+ \to \mathbb{R}^+$ one can define $$
f_\gamma (X) = \sum_{\alpha \in \mathrm{Mod} . \gamma} ...
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Ricci curvature of the Weil-Petersson metric?
Let $\omega_{\text{WP}}$ denote the Weil-Petersson metric associated to a family of Calabi-Yau manifolds. That is, let $f : X \to Y$ be a surjective holomorphic map with connected fibres such that, ...
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Weil-Petersson metric with respect to covering
Let $S$ be a closed oriented surface of genus $g\geq 2$. Consider the Teichmuller space $T(S)$. Let $d_t$ be the Teichmuller metric and $d_{WP}$ be the Weil-Petersson metric on $T(S)$. Let $P:S_1\...
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Weil-Petersson norm of a Beltrami form
I'm reading Scott Wolpert's paper Noncompleteness of the Weil-Petersson metric for Teichmüller Space.
He defines a path leading to the boundary of Teichmüller Space by giving surfaces $R_t$ ...
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Is Teichmüller distance bigger than Weil-Petersson distance on Teichmüller space?
It is known that Teichmüller distance ($d_{Teich}$) on Teichmüller space is complete, whereas Weil-Petersson distance ($d_{WP}$) is not complete.
See for example the article
Wolpert, Scott. ...
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Narasimhan-Simha Hermitian metric vs Weil-Petersson metric
What is relation between Weil-Petersson metric on holomorphic fibre space $f:X\to Y$ of compact complex manifolds $X,Y$ . (let fibres are Calabi-Yau manifolds)
And Ricci curvature of Narasimhan-Simha ...
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Moduli space of log Calabi-Yau varieties exists?
Let $\mathcal M^{(X,D)}$ be a moduli space of pair varieties $(X,D)$ which $K_X+D$ is trivial and $D$ is a divisor with conic singularities on Kaehler variety $X$. I am looking for a proof that such ...