相关论文: Weil-Petersson geometry and determinant bundles on…

There exists on each Teichm\"uller space $T_g$ (comprising compact Riemann surfaces of genus $g$), a natural sequence of determinant (of cohomology) line bundles, $DET_n$, related to each other via certain ``Mumford isomorphisms''. There is…

If $p : Y \to X$ is an unramified covering map between two compact oriented surfaces of genus at least two, then it is proved that the embedding map, corresponding to $p$, from the Teichm\"uller space ${\cal T}(X)$, for $X$, to ${\cal…

Let $\Mg$ denote the moduli space of compact Riemann surfaces of genus $g$. Mumford had proved that, for each fixed genus $g$, there are isomorphisms asserting that certain higher $DET$ bundles over $\Mg$ are certain fixed…

It is known that every finitely unbranched covering $\alpha:\widetilde{S}_{g(\alpha)}\rightarrow S$ of a compact Riemann surface $S$ with genus $g\geq2$ induces an isometric embedding $\Gamma_{\alpha}$ from the Teichm\"uller space $T(S)$ to…

In this article, we derive estimates of Teichm\"uller modular forms, and associated invariants. Let $\mathcal{M}_{g}$ denote the moduli space of compact hyperbolic Riemann surfaces of genus $g\geq 2$, and let $\overline{M}_{g}$ be the…

For a Riemann surface $X$ and the moduli of regularly stable $G$-bundles $M$, there is a naturally occuring "$adjoint$" vector bundle over $X \times M$. One can take the determinant of this vector bundle with respect to the projection map…

We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic threefold. In some cases, our invariants provide lower bounds for…

We prove that the universal Teichmuller space T(1) carries a new structure of a complex Hilbert manifold. We show that the connected component of the identity of T(1), the Hilbert submanifold T_{0}(1), is a topological group. We define a…

The Weil-Petersson and Takhtajan-Zograf metrics on the Riemann moduli spaces of complex structures for an $n$-fold punctured oriented surface of genus $g,$ in the stable range $g+2n>2,$ are shown here to have complete asymptotic expansions…

Over the past two decades the theory of the Weil-Petersson metric has been extended to general Teichm\"uller spaces of infinite type, including for example the universal Teichm\"uller space. In this paper we give a survey of the main…

In [4], Z. Huang showed that in the thick part of the moduli space $\mathcal{M}_g$ of compact Riemann surfaces of genus $g$, the sectional curvature of the Weil--Petersson metric is bounded below by a constant depending on injectivity…

The universal Teichm\"uller space is an infinitely dimensional generalization of the classical Teichm\"uller space of Riemann surfaces. It carries a natural Hilbert structure, on which one can define a natural Riemannian metric, the…

We construct an Ahlfors-Bers complex analytic model for the Teichm\"uller space of the universal hyperbolic lamination (also known as Sullivan's Teichm\"uller space) and the renormalized Weil-Petersson metric on it as an extension of the…

We construct a Petersson-Weil type K\"ahler form on the moduli spaces of Higgs bundles over a compact K\"ahler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature…

The self-duality equations on a Riemann surface arise as dimensional reduction of self-dual Yang-Mills equations. Hitchin had showed that the moduli space ${\mathcal M}$ of solutions of the self-duality equations on a compact Riemann…

Uniform bounds are developed for derivatives of solutions of the $2$-dimensional constant negative curvature equation and the Weil-Petersson metric for the Teichm\"{u}ller and moduli spaces. The dependence of the bounds on the geometry of…

We first give an exposition of how the Polyakov path integral for the bosonic string produces a natural mapping class group invariant measure, $d(Poly)$, on the Teichm\"uller space of Riemann surfaces of each fixed genus. The description of…

We investigate stable holomorphic vector bundles on a compact complex K\"ahler manifold and more generally on an orbifold that is equipped with a K\"ahler structure. We use the existence of Hermite-Einstein connections in this set-up and…

Let $\Sigma$ be a Riemann surface of genus $g$ bordered by $n$ curves homeomorphic to the circle $\mathbb{S}^1$, and assume that $2g+2-n>0$. For such bordered Riemann surfaces, the authors have previously defined a Teichm\"uller space which…

We prove a semisimplicity result for the boundary, in the corresponding Deligne-Mumford compactification, of a totally geodesic subvariety of a moduli space of Riemann surfaces. At the level of Teichm\"uller space, this semisimplicity…