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Thursday, April 23, 2020 | History

3 edition of Kahler Metric and Moduli Spaces (Advanced Studies in Pure Mathematics) found in the catalog.

Kahler Metric and Moduli Spaces (Advanced Studies in Pure Mathematics)

T. Ochiai

Kahler Metric and Moduli Spaces (Advanced Studies in Pure Mathematics)

  • 290 Want to read
  • 9 Currently reading

Published by Academic Press .
Written in English

    Subjects:
  • Differential & Riemannian geometry,
  • General,
  • Differential Geometry,
  • Mathematics,
  • Science/Mathematics

  • The Physical Object
    FormatHardcover
    Number of Pages448
    ID Numbers
    Open LibraryOL10069801M
    ISBN 100120010119
    ISBN 109780120010110

    Every K3 surface is Kählerian, i.e., admits a Kähler metric (Siu). Any two smooth K3 surfaces are deformation equivalent, hence diffeomorphic (Kodaira). The moduli space of holomorphic structures on a K3 surface is $20$-dimensional, and admits a branched covering by a ball in $\Cpx^{20}$ (Siu). The PI will investigate the following projects, all of which emerge from the study of the algebraic/analytic aspects of the moduli spaces. First, he will study the geometry of the moduli space of polarized Kahler manifolds via algebraic and analytic means (e.g., the positivity of the line bundles and heights over the moduli space).


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Kahler Metric and Moduli Spaces (Advanced Studies in Pure Mathematics) by T. Ochiai Download PDF EPUB FB2

Kähler Metric and Moduli Spaces, Volume II covers survey notes from the expository lectures given during the seminars in the academic year of for graduate students and mature mathematicians who were not experts on the topics considered during the sessions about partial differential Edition: 1.

Kähler Metric and Moduli Spaces: Advanced Studies in Pure Mathematics, Volume II Paperback – Novem by T. Ochiai (Editor) See all 2 formats and editions Hide other formats and editions. Price New from Used from Format: Paperback.

Kähler Metric and Moduli Spaces: Advanced Studies in Pure Mathematics, Vol. - Kindle edition by T. Ochiai. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Kähler Metric and Moduli Spaces: Advanced Studies in Pure Mathematics, Vol.

Kähler Metric and Moduli Spaces, Volume II covers survey notes from the expository lectures given during the Kahler Metric and Moduli Spaces book in the academic year of for graduate students and mature mathematicians who were not experts on the topics considered during the sessions about partial differential equations.

Kähler metric and moduli spaces. [Takushiro Ochiai;] Einstein-Kahler metrics with positive curvature, Einstein-Kahler metrics with non-positive Ricci Kahler Metric and Moduli Spaces book, A. Futaki et al; compact Ricci-Flat Kahler manifolds, I. Enoki; on the tangent sheaves on minimal varieties, K.

Sugiyama; Einstein-Kahler metrics on negative Ricci curvature on. Kähler Metric and Moduli Spaces, Is Part 2 Advanced studies in pure mathematics, ISSN Kähler Metric and Moduli Spaces, Takushiro Ochiai: Editor: Takushiro Ochiai: Publisher: Academic Press, ISBN: Kahler Metric and Moduli Spaces book, Length: pages: Export Citation: BiBTeX EndNote RefMan.

THE MODULI SPACE OF YANG-MILLS CONNECTIONS OVER A KAHLER SURFACE IS A COMPLEX MANIFOLD MITSUHIRO ITOH (Received J ) 1. Introduction Let M be a compact, connected, oriented Riemannian 4-manifold. Let P be a smooth principal G-bundle over M. For simplicity we assume that the Lie group G=SU(n), n^2. An St/^-connection A on P is called self.

This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind.

), the following theorem give an answer for finding canonical metric by using Song-Tian program in the case when the log-Kodaira dimension κ(X,D) is −∞. We can introduce the logarithmic Weil-Petersson metric on moduli space of log Fano varieties. Let Mn be the space of all n-dimensional Kahler-Einstein Fano manifolds, normalized so that Author: Hassan Jolany.

KAHLER GEOMETRY OF DOUADY SPACES˜ REYNIR AXELSSON AND GEORG SCHUMACHER 1. Abstract We consider the generalized Petersson-Weil metric on the moduli space of compact submanifolds of Kahler Metric and Moduli Spaces book K˜ahler manifold or a projective variety.

It is extended as a positive current to the space of points corresponding to reduced flbers, and estimates are shown. metric. Kahler manifolds are modelled on complex Euclidean space. Except for the latter, the main example is complex projective space endowed with the Fubini–Study metric.

Let N be a complex submanifold of a Kahler manifold M. Since the re-striction of the Riemannian metric of M to N is Hermitian and its Kahler. of moduli space of Kahler manifolds admitting constant scalar curvature Kahler (cscK) metrics. They proved that the natural Weil-Petersson metric is always Kahler by interpreting it as the Chern curvature of a determinant line bundle equipped with Quillen metric.

As a consequence, it wasFile Size: KB. Kahler Metric and Moduli Spaces book This book is an exposition of what is currently known about the fundamental groups of compact Kahler manifolds.

This class of groups contains all finite groups and is strictly smaller than the. Theorem (K¨ahler hyperbolic) The Teichmu¨ller metric on moduli space is comparable to a K¨ahler metric h such that (M g,n,h) is K¨ahler hyperbolic. The bass note of Teichmul¨ ler space. The universal cover of M g,n is the Teichmu¨ller space T g,n.

Recall Kahler Metric and Moduli Spaces book the Teichmulle¨ r metric gives norms ## T on the tangent and cotangent. The deviation of a Riemannian manifold X from the standard metric on Euclidean space is measured by sectional curvature, which is a real number associated to any real 2-plane in the tangent space of X at a point.

For example, the sectional curvature of the standard metric on CP n (for n. pactifications of moduli spaces of Kahler-Einstein Fano manifolds in all complex dimensions bigger than two (Fano K-moduli spaces). We also discuss potential ap-plications to explicit study of moduli spaces of K-stable Fano manifolds with large anti-canonical volume.

Our arguments are based on recent progress about the ge-ometry of metric File Size: KB. such manifolds, and finite volume quotients of Hermitian symmetric spaces with no compact or Euclidean factors [Gr]. In this paper we show: Theorem (K¨ahler hyperbolic) The Teichmu¨ller metric on moduli space is comparable to a Kahl¨ er metric h such that (M g,n,h) is Kahl¨ er hyperbolic.

The bass note of Teichmu¨ller space. Donaldson conjectured [16] that the space of Kähler metrics is geodesically convex by smooth geodesics and that it is a metric space.

Following Donaldson's program, we verify the second part of Donaldson's conjecture completely and verify his first part partially. PDF | On Jan 1,Georg Schumacher and others published The Theory of Teichmuller Spaces { A View Towards Moduli Spaces of Kahler Manifolds | Find, read and cite all the research you need on Author: Georg Schumacher.

The Petersson-Weil metric is a main tool for investigating the geometry of moduli spaces. When A. Weil considered the classical Teichmüller space from the viewpoint of deformation theory, he suggested, ininvestigating the Petersson inner product on the space of holomorphic quadratic by: a later paper, in particular their possible relation to the moduli space of monopoles in [R3.

The Metric and the Twistor Space We shall review briefly the work of Hitchin et al. [1 1, 6]: Let M be a 4n-dimensional hyper-Kahler manifold with a free action of ίRn on it. It is assumed that this action extends to a free holomorphic action of C.

The Teichmuller metric on moduli˜ space is comparable to a Kahler metric˜ hsuch that (M g;n;h) is Kahler hyper-˜ bolic. The bass note of Teichmuller space.˜ The universal cover of M g;nis the Teichm˜uller space T g;n.

Recall that the Teichm˜uller metric gives norms k¢k T on the tangent and cotangent bundles to T g;n. The analogue of the. AND KAHLER METRICS ON MODULI SPACES UDC + N. IVANOV ABSTRACT. This paper deals mainly with the geometrical and topological aspects of the connection recently discovered by Zograf and Takhtadzhyan between the acces-sory parameters of Schwarzian differential equations and the Weil-Petersson metric on Teichmuller by: The quotient of the Teichmüller space T g,n by the action of the mapping class group is the moduli space of Riemann surfaces M g,n ; the Weil-Petersson metric is mapping class group invariant and Author: Curtis T.

Mcmullen. stable vector bundles on a K3-surface with hyper-Kahler structure is given, and this metric is extended to the compactification of the moduli space by torsion-free sheaves. INTRODUCTION The moduli space of stable vector bundles on a compact Kahler surface (S, ω) has a canonical Kahler metric, which it is natural to call the Weil-Petersson.

There exists a Kahler metric on moduli space of Calabi-Yau varieties we call it again Weil Petersson metric and can be written as Ricci curvature of direct image of relative Line bundle. Fujiki-Schumacher considered the moduli space of Kahler manifolds admitting constant scalar curvature Kahler (cscK) metrics.

In these examples we compute the Kaehler class of the natural L^2-metric on the moduli space. In the simplest cases we compute the volume and total scalar curvature of the muduli space.

Finally, we note that for abelian GLSM the vortex moduli space is a compactification of the space of holomorphic maps from M to toric targets, just as in the. In fact by knowing this fact we can construct a canonical Weil-Petersson metric on moduli space of Kahler-Einstein Fano varieties with mild singularities aic-geometry complex-geometry moduli-spaces kahler-manifolds minimal-model-program.

THEOREM (Kahler hyperbolic). The Teichmiiller metric on moduli space is comparable to a Kihler metric h such that (Mg,n, h) is Kihler hyper-bolic. The bass note of Teichmiiller space.

The universal cover of Mg,n is the Teichmiiller space Tg,n- Recall that the Teichmiiller metric gives norms 11 I IT on the tangent and cotangent bundles to Tg,n. Metrics and Special Kahler Geometry on the Moduli Spaces of Higgs Bundles and Hitchin Systems: Author: Huang, Zhenxi: Issue Date: School/Discipline: School of Mathematical Sciences: Abstract: The notions of Hitchin systems and Higgs bundles (also called Higgs pairs) were Author: Zhenxi Huang.

This proportionality is an analogue of the Einstein field equation in general relativity. The following conjecture is due to E. Calabi: Let be a compact connected complex manifold and its first Chern class; then. a) if, then carries a unique (Ricci-negative) Kähler–Einstein metric such that.

b) if, then any Kähler class of admits a unique (Ricci-flat) Kähler–Einstein metric such. Let $\cM_{g,n}$ be the moduli space of Riemann surfaces of genus $g$ with $n$ punctures.

From a complex perspective, moduli space is hyperbolic. For example. For compact Riemann surfaces of genus at least two, using Petersson’s Hermitian pairing for automorphic forms, Weil introduced a Hermitian metric for the Teiclmüller space, now known as the Weil-Petersson metric.

Ahlfors [1,2] showed that the Weil-Petersson metric is Kähler and that its Ricci and holomorphic section curvatures are by: Abstract. Metric deformation methods are used to give a more geometric proof of the well known Calabi conjectures of Kahler geometry.

More precisely, it is proven that given any closed (1,1) form on a compact Kahler manifold M, which represents the first Chern class of M, one can deform the initial metric by certain Hamilton's type equation to the limit Kahler metric which has the given (1,1. Moduli spaces of sheaves of rank 2 on a surface are not smooth, unless we consider sheaves with special invariants on special surfaces.

Nevertheless, something is known about the type of singularities they can attain. Concerning the geometry of moduli spaces of sheaves of higher rank, there are two guiding principles for the investigation. ries and the Seiberg-Witten solution.

For local special geometry, we study their emergence in N = 2;d = 4 supergravity and Calabi-Yau moduli space. In particular, we discuss the connection between string effective action and the metric on Calabi-Yau moduli space, and the non-renormalization theorem of type IIB complex moduli space.

Finally File Size: KB. AUGMENTED WEIL-PETERSSON METRICS ON MODULI SPACES 3 Then S admits a C1augmented Weil-Petersson metric whose holomorphic sectional curvature is bounded above by a negative constant.

The de nitions needed for the more general setting of Theorem 1’ will be given in Section 5. We remark that while Theorem 1’ covers the case of The. In these examples we compute the Kaehler class of the natural L^2-metric on the moduli space.

In the simplest cases we compute the volume and total scalar curvature of the muduli space. Finally, we note that for abelian GLSM the vortex moduli space is a compactification of the space of holomorphic maps from M to toric targets, just as in the Cited by: 4.

QUASI-PROJECTIVITY OF THE MODULI SPACE OF SMOOTH KAHLER-EINSTEIN FANO MANIFOLDS CHI LI, XIAOWEI WANG, AND CHENYANG XU Abstract. In this note, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space Mof smoothable K ahler-Einstein Fano varieties.

In the study of the moduli space Mg (and the Teichmüller space Tg) of compact Riemann surfaces of genus g >2, the Weil-Petersson metric plays an important role, and it has been widely studied. In particular, Ahlfors ([Ahl61], [Ahl62]) showed that the Weil-Petersson metric on Tg is a Kahler metric.

Quaternionic structure. Every hyperkähler manifold M has pdf 2-sphere of complex structures (i.e. pdf almost complex structures) with respect to which the metric is Kähler.

In particular, it is a hypercomplex manifold, meaning that there are three distinct complex structures, I, J, and K, which satisfy the quaternion relations = = = = − Any linear combination.Compact Download pdf space of Fano Kahler-Einstein varieties In this talk, I will survey our construction of a compact moduli space of Fano KE varieties, this is based on the joint work with Chi Li and Chenyang Xu.

This talk is postponed to Fall Thursday, Ma pm, roomDouble Header: Zuoqin Wang (USTC/MIT).The Mathematical Sciences Research Institute (MSRI), founded inis an independent ebook mathematical research institution whose funding ebook include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions.

The Institute is located at 17 Gauss Way, on the University of California, Berkeley campus, close to Grizzly Peak, on the.