Last edited by Brall
Tuesday, July 28, 2020 | History

7 edition of The Hodge Theory of Projective Manifolds found in the catalog.

The Hodge Theory of Projective Manifolds

by Mark Andrea De Cataldo

  • 351 Want to read
  • 27 Currently reading

Published by Imperial College Press .
Written in English

    Subjects:
  • Algebraic geometry,
  • Science,
  • Mathematics,
  • Science/Mathematics,
  • Algebra - General,
  • Topology - General,
  • Science / Mathematics,
  • System Theory

  • The Physical Object
    FormatHardcover
    Number of Pages116
    ID Numbers
    Open LibraryOL12055611M
    ISBN 101860948006
    ISBN 109781860948008

    The curvature K of a surface depends only on the coefficients g ij of the first fundamental form and their first- and second-order derivatives. Therefore K is an intrinsic property of the surface.. Theorema egregium of Gauss () His spirit lifted the deepest secrets of numbers, space, and nature; he measured the orbits of the planets, the form and the forces of the earth; in his mind he. K-equivalent complex projective manifolds have the same Betti numbers by using the theory of p-adic integrals and Deligne’s so-lution to the Weil conjecture. The aim of this note is to show that with a little more book-keeping work, namely by applying Faltings’ p-adic Hodge Theory, our p-adic method also leads to the equiva-.

    compact K ahler manifolds. Hodge theory, named after W.V.D. Hodge, is a branch of mathematics belonging to both algebraic topology and di erential geometry that enables us to nd topological information about a smooth or complex manifold from the study of di erential forms and di erential operators on these manifolds. ics developed include Hodge’s theory of harmonic integrals and Kodaira’s characterization of projective algebraic manifolds. This book should be suitable for a graduate level course on the general topic of complex manifolds. I have avoided developing any of the theory of several complex variables relating to recent developments in Stein.

    A simple consequence of Hodge theory is that every odd Betti number b 2a+1 of a compact Kähler manifold is even, by Hodge symmetry. This is not true for compact complex manifolds in general, as shown by the example of the Hopf surface, which is diffeomorphic to S 1 × S 3 and hence has b 1 = 1. Theorem, Section 5 - degeneracy of the Hodge to de Rham spectral sequence). Moreover, we will discuss the Hodge Theorem and Hodge decomposition for the cohomology of a compact, K ahler manifold and thus for a smooth projective complex variety. We begin with stating some known facts in Section 2, which serves an introductory purpose.


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The Hodge Theory of Projective Manifolds by Mark Andrea De Cataldo Download PDF EPUB FB2

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the The Hodge Theory of Projective Manifolds book becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds.

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective by: 5.

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds.

"This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kahler, to complex projective manifolds.

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds.

Abstract. This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective by: 5.

INTRODUCTION TO HODGE THEORY 3 The decomposition () has the property of Hodge symmetry Λp,qT∗X= Λq,pT∗X, where complex conjugation acts naturally on ΛkT∗X⊗C.

If we let Ek(X)C denote the space of complex differential forms of degree on X, i.e. the C∞-sections of the vector bundle ΛkT∗X⊗C, then we also have the exterior differential d: Ek(X)C → Ek+1(X)C.

Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc. Search. Quick Search anywhere. Enter words / phrases / DOI / ISBN / keywords / authors / etc. Search. Quick search in Citations.

Journal Year Volume Issue Page. Search. Advanced. This thesis is concerned with the topology and geometry of Sasakian manifolds. Sasaki structures consist of certain contact forms equipped with special Riemannian metrics. Sasakian manifolds relate to arbitrary contact manifolds as Kählerian or projective complex manifolds relate to arbitrary symplectic manifolds.

Therefore, Sasakian manifolds are the odd-dimensional analogs of Kähler manifolds. This is a written-up version of eight introductory lectures to the Hodge theory of projective manifolds.

The table of contents should be self-explanatory. What kind of an answer are you looking for. It’s hard to answer a question like this in the abstract without knowing anything about you/your background knowledge etc. I’m going to assume your question is really “what are some good introductory ref.

From the June Summer School come 20 contributions that explore algebraic cycles (a subfield of algebraic geometry) from a variety of perspectives.

The papers have been organized into sections on cohomological methods, Chow groups and motives, and arithmetic methods. Some specific topics include logarithmic Hodge structures and classifying spaces; Bloch's conjecture and the K-theory.

This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem.

We determine the structure of the Hodge ring, a natural object encoding the Hodge numbers of all compact Kähler manifolds. As a consequence of this structure, there are no unexpected relations among the Hodge numbers, and no essential differences between the Hodge numbers of smooth complex projective varieties and those of arbitrary Kähler manifolds.

The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers.

The new families are determined by combining and generalizing two The Galois Group Decomposition of the Hodge Structure. A basic application of Hodge theory is that the odd Betti numbers b 2a+1 of a smooth complex projective variety (or compact Kähler manifold) are even, by Hodge is not true for compact complex manifolds in general, as shown by the example of the Hopf surface, which is diffeomorphic to S 1 × S 3 and hence has b 1 = The "Kähler package" is a powerful set of.

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 class of all finitely presentable groups.

For the first time ever, this book collects together all the results obtained in the last few years which aim to characterise those infinite groups which can.

The Fubini-Study metric on CPn; projective complex manifolds are Kähler. Exterior forms on Kähler manifolds, the operators ∂*, ∂*,L,Λ. The Kähler identities.

\textbf{Lecture 5}: Hodge theory for Kähler manifolds. Summary of Hodge theory for compact Riemannian manifolds. Hodge theory for Kähler manifolds. This book contains a focused introduction into the theory of K ahler manifolds.

The main result is Kodaira’s embedding theorem which characterizes compact complex manifolds that are biholomorphic equivalent to a projective algebraic manifold.

The necessary and su cient condition is the existence of a positive holomorphic line bundle. The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated.

K ahler manifold is K ahler. Consequently, because projective varieties are closed subspaces of projective spaces, projective varieties are all K ahler.

This explains why Hodge’s original interest in projective varieties was replaced by the general K ahler manifolds. Theorem (The Hodge Decomposition). Let Xbe a compact K ahler man-ifold.Hodge Structure (VHS) at the ICTP Summer School on Hodge Theory.

The modern theory of variations of Hodge structure (although some authors have referred to this period as the pre-history) begins with the work of Gri ths [23, 24, 25] and continues with that of Deligne [17, 18, 19], and Schmid [41]. The basic object of.acccounts of basic Hodge theory can be found in the books of Griffiths-Harris [GH], Warner [Wa] and Wells [W].

However, we will depart slightly from these treatments by outling the heat equation method of Milgram and Rosenbloom [MR]. This is an elegant and comparatively elementary approach to the Hodge .