Related papers: A period mapping in universal Teichm\"uller space

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 commensurable to an arithmetic subgroup in SO(3,…

We study the period map from infinitesimal deformations of a scheme $X$ over a perfect field $k$ to those of the associated $k$-linear $\infty$-category $\mathrm{QC}(X)$. For quasicompact, smooth, and separated $X$, we identify the…

Let $T$ be a torus of dimension $n>1$ and $M$ a compact $T-$manifold. $M$ is a GKM manifold if the set of zero dimensional orbits in the orbit space $M/T$ is zero dimensional and the set of one dimensional orbits in $M/T$ is one…

We prove that the space of convex real projective structures on a surface of genus $g\ge 2$ admits a mapping class group invariant K\"ahler metric where Teichm\"uller space with Weil-Petersson metric is a totally geodesic complex…

We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichm\"uller Space: (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The…

We describe the proof that the period map from the Torelli space of Calabi-Yau manifolds to the classifying space of polarized Hodge structures is an embedding. The proof is based on the constructions of holomorphic affine structure on the…

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…

Let M be the moduli space of irreducible flat PSL(2,R) connections on a punctured surface of finite type with parabolic holonomies around punctures. By using a notion of admissibility of an ideal arc, M is covered by dense open subsets…

Lipman Bers' universal Teichm\"uller space, classically denoted by $T(1)$, plays a significant role in Teichm\"uller theory, because all the Teichm\"uller spaces $T(G)$ of Fuchsian groups $G$ can be embedded into it as complex submanifolds.…

We study the curvature of the moduli space M_g of curves of genus g with the Siegel metric induced by the period map. We give an explicit formula for the holomorphic sectional curvature of M_g along a Schiffer variation at a point P on the…

We give an explicit decription for univeral principal U(r)-bundles with periodic map by means of equivariant Stiefel manifolds. We then show that the associated equivariant vector bundle is equivalent to the canonical one given by G. Segal.…

This paper is a comprehensive introduction to the results of [7]. It grew as an expanded version of a talk given at INdAM Meeting Complex and Symplectic Geometry, held at Cortona in June 12-18, 2016. It deals with the construction of the…

We prove a regularity theorem for harmonic maps into Teichm\"uller space. More specifically, if $u$ is a harmonic map from a Riemannian domain to the metric completion of Teichm\"uller space with respect to the Weil-Petersson metric, and…

A Teichm\"uller space $Teich$ is a quotient of the space of all complex structures on a given manifold $M$ by the connected components of the group of diffeomorphisms. The mapping class group $\Gamma$ of $M$ is the group of connected…

The loop space $L\mathbb{P}^n$ of the complex projective space $\mathbb{P}^n$ consisting of all $C^k$ or Sobolev $W^{k, \, p}$ maps $S^1 \to \mathbb{P}^n$ is an infinite dimensional complex manifold. We identify a class of holomorphic…

The period morphism of polarized hyper-K\"ahler manifolds of K3$^{[m]}$-type gives an embedding of each connected component of the moduli space of polarized hyper-K\"ahler manifolds of K3$^{[m]}$-type into their period space, which is the…

The total space of the tangent bundle of a K\"ahler manifold admits a canonical K\"ahler structure. Parallel translation identifies the space ${\Bbb{T}}$ of oriented affine lines in ${\Bbb{R}}^3$ with the tangent bundle of $S^2$. Thus, the…

In this paper, we construct the moduli space of marked oper structures on a closed, oriented smooth surface of negative Euler characteristic as a holomorphic fiber bundle over Teichm\"{u}ller space. We prove that the holonomy map from the…

There are several Teichm\"uller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal…

Let $S$ be a closed, orientable surface of genus at least 2. The cotangent bundle of the "hyperbolic'' Teichm\"uller space of $S$ can be identified with the space $\CP$ of complex projective structures on $S$ through measured laminations,…