scholarly journals Boundary Behaviour of Weil–Petersson and Fibre Metrics for Riemann Moduli Spaces

2017 ◽  
Vol 2019 (16) ◽  
pp. 5012-5065 ◽  
Author(s):  
Richard Melrose ◽  
Xuwen Zhu
Keyword(s):  
Moduli Spaces ◽  
Asymptotic Expansions ◽  
Conformal Factor ◽  
Complex Structures ◽  
Stable Range ◽  
Universal Curve ◽  
Boundary Behaviour ◽  
Hyperbolic Metrics ◽  
Push Forward ◽  
Complete Metrics

Abstract 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 in terms of Fenchel–Nielsen coordinates at the exceptional divisors of the Knudsen–Deligne–Mumford compactification. This is accomplished by finding a full expansion for the hyperbolic metrics on the fibres of the universal curve as they approach the complete metrics on the nodal curves above the exceptional divisors and then using a push-forward theorem for conormal densities. This refines a two-term expansion due to Obitsu–Wolpert for the conformal factor relative to the model plumbing metric which in turn refined the bound obtained by Masur. A similar expansion for the Ricci metric is also obtained.

NEW POLARIZATIONS ON THE MODULI SPACES AND THE THURSTON COMPACTIFICATION OF TEICHMÜLLER SPACE

1998 ◽  
Vol 09 (01) ◽  
pp. 1-45 ◽  
Author(s):  
JØRGEN ELLEGAARD ANDERSEN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Teichmüller Space ◽  
Closed Surface ◽  
Teichmuller Space ◽  
Open Dense Subset ◽  
Complex Structures ◽  
Thurston Boundary ◽  
Simply Connected ◽  
Singular Metric

Given a foliation F with closed leaves and with certain kinds of singularities on an oriented closed surface Σ, we construct in this paper an isotropic foliation on ℳ(Σ), the moduli space of flat G-connections, for G any compact simple simply connected Lie-group. We describe the infinitesimal structure of this isotropic foliation in terms of the basic cohomology with twisted coefficients of F. For any pair (F, g), where g is a singular metric on Σ compatible with F, we construct a new polarization on the symplectic manifold ℳ′(Σ), the open dense subset of smooth points of ℳ(Σ). We construct a sequence of complex structures on Σ, such that the corresponding complex structures on ℳ′(Σ) converges to the polarization associated to (F, g). In particular we see that the Jeffrey–Weitzman polarization on the SU(2)-moduli space is the limit of a sequence of complex structures induced from a degenerating family of complex structures on Σ, which converges to a point in the Thurston boundary of Teichmüller space of Σ. As a corollary of the above constructions, we establish a certain discontinuiuty at the Thurston boundary of Teichmüller space for the map from Teichmüller space to the space of polarizations on ℳ′(Σ). For any reducible finite order diffeomorphism of the surface, our constuction produces an invariant polarization on the moduli space.

scholarly journals Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle

2019 ◽  
Vol 2019 (749) ◽  
pp. 87-132
Author(s):  
Laurent Meersseman
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Classical Case ◽  
Analytic Space ◽  
Fundamental Result ◽  
Compact Complex Manifold ◽  
Complex Structures ◽  
Analogous Statement ◽  
Finite Dimensional ◽  
Cr Structures

Abstract Kuranishi’s fundamental result (1962) associates to any compact complex manifold {X_{0}} a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to {X_{0}} . In this paper, we give an analogous statement for Levi-flat CR-manifolds fibering properly over the circle by associating to any such {\mathcal{X}_{0}} the loop space of a finite-dimensional analytic space which serves as a local moduli space of CR-structures close to {\mathcal{X}_{0}} . We then develop in this context a Kodaira–Spencer deformation theory making clear the likenesses as well as the differences with the classical case. The article ends with applications and examples.

scholarly journals Stable maps and stable quotients

2014 ◽  
Vol 150 (9) ◽  
pp. 1457-1481 ◽  
Author(s):  
Cristina Manolache
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Stable Maps ◽  
Intersection Numbers ◽  
Fundamental Class ◽  
Push Forward ◽  
The Relationship

AbstractWe analyze the relationship between two compactifications of the moduli space of maps from curves to a Grassmannian: the Kontsevich moduli space of stable maps and the Marian–Oprea–Pandharipande moduli space of stable quotients. We construct a moduli space which dominates both the moduli space of stable maps to a Grassmannian and the moduli space of stable quotients, and equip our moduli space with a virtual fundamental class. We relate the virtual fundamental classes of all three moduli spaces using the virtual push-forward formula. This gives a new proof of a theorem of Marian–Oprea–Pandharipande: that enumerative invariants defined as intersection numbers in the stable quotient moduli space coincide with Gromov–Witten invariants.

scholarly journals GEOMETRY OF THE MODULI OF HIGHER SPIN CURVES

2000 ◽  
Vol 11 (05) ◽  
pp. 637-663 ◽  
Author(s):  
TYLER J. JARVIS
Keyword(s):  
Line Bundle ◽  
Moduli Spaces ◽  
Disjoint Union ◽  
Algebraic Curves ◽  
Quantum Cohomology ◽  
Smooth Curve ◽  
Natural Generalization ◽  
Intersection Theory ◽  
Universal Curve ◽  
Irreducible Components

This article treats various aspects of the geometry of the moduli [Formula: see text] of r-spin curves and its compactification [Formula: see text]. Generalized spin curves, or r-spin curves, are a natural generalization of 2-spin curves (algebraic curves with a theta-characteristic), and have been of interest lately because of the similarities between the intersection theory of these moduli spaces and that of the moduli of stable maps. In particular, these spaces are the subject of a remarkable conjecture of E. Witten relating their intersection theory to the Gelfand–Dikii (KdVr) heirarchy. There is also a W-algebra conjecture for these spaces [16] generalizing the Virasoro conjecture of quantum cohomology. For any line bundle [Formula: see text] on the universal curve over the stack of stable curves, there is a smooth stack [Formula: see text] of triples (X, ℒ, b) of a smooth curve X, a line bundle ℒ on X, and an isomorphism [Formula: see text]. In the special case that [Formula: see text] is the relative dualizing sheaf, then [Formula: see text] is the stack [Formula: see text] of r-spin curves. We construct a smooth compactification [Formula: see text] of the stack [Formula: see text], describe the geometric meaning of its points, and prove that its coarse moduli is projective. We also prove that when r is odd and g>1, the compactified stack of spin curves [Formula: see text] and its coarse moduli space [Formula: see text] are irreducible, and when r is even and [Formula: see text] is the disjoint union of two irreducible components. We give similar results for n-pointed spin curves, as required for Witten's conjecture, and also generalize to the n-pointed case the classical fact that when [Formula: see text] is the disjoint union of d(r) components, where d(r) is the number of positive divisors of r. These irreducibility properties are important in the study of the Picard group of [Formula: see text] [15], and also in the study of the cohomological field theory related to Witten's conjecture [16, 34].

scholarly journals Generalized punctual Hilbert schemes and 𝔤-complex structures

2021 ◽  
Author(s):  
Alexander Thomas
Keyword(s):  
Lie Algebras ◽  
Moduli Spaces ◽  
Hilbert Scheme ◽  
Complex Structure ◽  
Complex Structures ◽  
Hilbert Schemes ◽  
Simple Complex ◽  
Geometric Structures ◽  
Punctual Hilbert Scheme ◽  
Alternative Description

We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple properties with Hitchin components, and which are conjecturally homeomorphic to them. For simple complex Lie algebras, this generalizes the higher complex structure. For real Lie algebras, this should give an alternative description of the Hitchin–Kostant–Rallis section.

scholarly journals Adapted complex structures and geometric quantization

1999 ◽  
Vol 154 ◽  
pp. 171-183 ◽  
Author(s):  
Róbert Szőke
Keyword(s):  
Symmetric Space ◽  
Tangent Bundle ◽  
Geodesic Flow ◽  
Symmetric Spaces ◽  
Complex Structure ◽  
Geometric Quantization ◽  
Riemannian Symmetric Space ◽  
Complex Structures ◽  
Rank One ◽  
Push Forward

AbstractA compact Riemannian symmetric space admits a canonical complexification. This so called adapted complex manifold structure JA is defined on the tangent bundle. For compact rank-one symmetric spaces another complex structure JS is defined on the punctured tangent bundle. This latter is used to quantize the geodesic flow for such manifolds. We show that the limit of the push forward of JA under an appropriate family of diffeomorphisms exists and agrees with JS.

Cell morphology, volume, and surface area determinations from multilevel contouring within HVEM micrographs of serial sections and whole-cell mounts

1987 ◽  
Vol 45 ◽  
pp. 588-589
Author(s):  
M. Marko ◽  
A. Leith ◽  
D. Parsons
Keyword(s):  
Surface Area ◽  
Electron Micrographs ◽  
Cell Morphology ◽  
Individual Variation ◽  
Serial Section ◽  
Stereo Pair ◽  
Complex Structures ◽  
Serial Sections ◽  
Surface Areas ◽  
Computer Based

The use of serial sections and computer-based 3-D reconstruction techniques affords an opportunity not only to visualize the shape and distribution of the structures being studied, but also to determine their volumes and surface areas. Up until now, this has been done using serial ultrathin sections.The serial-section approach differs from the stereo logical methods of Weibel in that it is based on the Information from a set of single, complete cells (or organelles) rather than on a random 2-dimensional sampling of a population of cells. Because of this, it can more easily provide absolute values of volume and surface area, especially for highly-complex structures. It also allows study of individual variation among the cells, and study of structures which occur only infrequently.We have developed a system for 3-D reconstruction of objects from stereo-pair electron micrographs of thick specimens.

Stereo modeling of HVEM specimens by serial tilting and computer graphics

1986 ◽  
Vol 44 ◽  
pp. 34-35
Author(s):  
J.R. McIntosh ◽  
D.L. Stemple ◽  
William Bishop ◽  
G.W. Hannaway
Keyword(s):  
Computer Graphics ◽  
Analytical Methods ◽  
Photographic Film ◽  
Complex Structures ◽  
Multiple Objects ◽  
Multiple Images ◽  
3 Dimensional

EM specimens often contain 3-dimensional information that is lost during micrography on a single photographic film. Two images of one specimen at appropriate orientations give a stereo view, but complex structures composed of multiple objects of graded density that superimpose in each projection are often difficult to decipher in stereo. Several analytical methods for 3-D reconstruction from multiple images of a serially tilted specimen are available, but they are all time-consuming and computationally intense.

EXELFS Studies of Carbon Fibers

1990 ◽  
Vol 48 (2) ◽  
pp. 72-73
Author(s):  
V. Serin ◽  
K. Hssein ◽  
G. Zanchi ◽  
J. Sévely
Keyword(s):  
Carbon Fibers ◽  
Energy Analysis ◽  
Electron Excitation ◽  
Complex Structures ◽  
High Modulus ◽  
Promising Technique ◽  
X Ray ◽  
Fine Structures ◽  
X Ray Absorption

The present developments of electron energy analysis in the microscopes by E.E.L.S. allow an accurate recording of the spectra and of their different complex structures associated with the inner shell electron excitation by the incident electrons (1). Among these structures, the Extended Energy Loss Fine Structures (EXELFS) are of particular interest. They are equivalent to the well known EXAFS oscillations in X-ray absorption spectroscopy. Due to the EELS characteristic, the Fourier analysis of EXELFS oscillations appears as a promising technique for the characterization of composite materials, the major constituents of which are low Z elements. Using EXELFS, we have developed a microstructural study of carbon fibers. This analysis concerns the carbon K edge, which appears in the spectra at 285 eV. The purpose of the paper is to compare the local short range order, determined by this way in the case of Courtauld HTS and P100 ex-polyacrylonitrile carbon fibers, which are high tensile strength (HTS) and high modulus (HM) fibers respectively.

Silicification of wood-cell walls

1994 ◽  
Vol 52 ◽  
pp. 428-429
Author(s):  
S. E. Keckler ◽  
D. M. Dabbs ◽  
N. Yao ◽  
I. A. Aksay
Keyword(s):  
Electron Microscopy ◽  
Cell Wall ◽  
Cell Walls ◽  
Lignin Content ◽  
Resin Composite ◽  
Middle Lamella ◽  
Cellulose Fibers ◽  
Complex Structures ◽  
Rich Region ◽  
Inorganic Precursors

Cellular organic structures such as wood can be used as scaffolds for the synthesis of complex structures of organic/ceramic nanocomposites. The wood cell is a fiber-reinforced resin composite of cellulose fibers in a lignin matrix. A single cell wall, containing several layers of different fiber orientations and lignin content, is separated from its neighboring wall by the middle lamella, a lignin-rich region. In order to achieve total mineralization, deposition on and in the cell wall must be achieved. Geological fossilization of wood occurs as permineralization (filling the void spaces with mineral) and petrifaction (mineralizing the cell wall as the organic component decays) through infiltration of wood with inorganics after growth. Conversely, living plants can incorporate inorganics into their cells and in some cases into the cell walls during growth. In a recent study, we mimicked geological fossilization by infiltrating inorganic precursors into wood cells in order to enhance the properties of wood. In the current work, we use electron microscopy to examine the structure of silica formed in the cell walls after infiltration of tetraethoxysilane (TEOS).

Sign in / Sign up

Export Citation Format

Share Document