Period Mappings and Period Domains

@inproceedings{Carlson2017PeriodMA,
  title={Period Mappings and Period Domains},
  author={James A. Carlson and Stefan M{\"u}ller–Stach and C. A. M. Peters},
  year={2017}
}
Part I. Basic Theory of the Period Map: 1. Introductory examples 2. Cohomology of compact Kahler manifolds 3. Holomorphic invariants and cohomology 4. Cohomology of manifolds varying in a family 5. Period maps looked at infinitesimally Part II. The Period Map: Algebraic Methods: 6. Spectral sequences 7. Koszul complexes and some applications 8. Further applications: Torelli theorems for hypersurfaces 9. Normal functions and their applications 10. Applications to algebraic cycles: Nori's theorem… 
Harmonic maps from K\"ahler manifolds
This report attempts a clean presentation of the theory of harmonic maps from complex and Kahler manifolds to Riemannian manifolds. After reviewing the theory of harmonic maps between Riemannian
Harmonic maps from Kähler manifolds
This report attempts a clean presentation of the theory of harmonic maps from complex and Kahler manifolds to Riemannian manifolds. After reviewing the theory of harmonic maps between Riemannian
Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations
We give a simple expression for the integral of the canonical holomorphic volume form in degenerating families of varieties constructed from wall structures and with central fiber a union of toric
Positivity of vector bundles and Hodge theory
Differential geometry, especially the use of curvature, plays a central role in modern Hodge theory. The vector bundles that occur in the theory (Hodge bundles) have metrics given by the
MODULI SPACES OF RIEMANN SURFACES
1. Different ways to build and deform Riemann surfaces 2 2. Teichmüller space and moduli space 4 3. The Deligne-Mumford compactification of moduli space 11 4. Jacobians, Hodge structures, and the
Jacobian rings for homogenous vector bundles and applications
In this note, we examine the Jacobian ring description of the Hodge structure of zero loci of vector bundle sections on a class of ambient varieties. We consider a set of cohomological vanishing
Geometric Variations of Local Systems and Elliptic Surfaces
Geometric variations of local systems are families of variations of Hodge structure; they typically correspond to fibrations of K\"{a}hler manifolds for which each fibre itself is fibred by
The global derived period map
Arakelov-Milnor inequalities and maximal variations of Hodge structure
In this paper we study the C∗-fixed points in moduli spaces of Higgs bundles over a compact Riemann surface for a complex semisimple Lie group and its real forms. These fixed points are called Hodge
The global asymptotic structure of period mappings
. This work is part of a project to construct completions of period mappings Φ : B → Γ \ D . A proper topological SBB-esque completion Φ 0 : B → ℘ 0 is constructed. The fibres of Φ 0 are projective
...
...

References

SHOWING 1-10 OF 325 REFERENCES
Compact complex surfaces.
Historical Note.- References.- The Content of the Book.- Standard Notations.- I. Preliminaries.- Topology and Algebra.- 1. Notations and Basic Facts.- 2. Some Properties of Bilinear forms.- 3. Vector
Algebraic Geometry: A First Course
1: Affine and Projective Varieties. 2: Regular Functions and Maps. 3: Cones, Projections, and More About Products. 4: Families and Parameter Spaces. 5: Ideals of Varieties, Irreducible Decomposition.
PERIODS OF INTEGRALS ON ALGEBRAIC MANIFOLDS, II
II. 0. Introduction. (a) The purpose of this paper is to study the local behavior of the periods of integrals, as functions of the parameters, in a family of polarized algebraic manifolds. The
Topological methods in algebraic geometry
Introduction Chapter 1: Preparatory material 1. Multiplicative sequences 2. Sheaves 3. Fibre bundles 4. Characteristic classes Chapter 2: The cobordism ring 5. Pontrjagin numbers 6. The ring
Quasi-projective moduli for polarized manifolds
  • E. Viehweg
  • Mathematics
    Ergebnisse der Mathematik und ihrer Grenzgebiete
  • 1995
This text discusses two subjects of quite different natures: construction methods for quotients of quasi-projective schemes either by group actions or by equivalence relations; and properties of
Infinitesimal variation of Hodge structures and the weak global Torelli theorem for complete intersections
In this paper, we will study the weak global Torelli theorem for complete intersections of hypersurfaces in a projective space. Let X be a non-singular projective variety of dimension r with an ample
A survey of the Hodge conjecture
Complex manifolds Vector bundles Kahler manifolds Line bundles The Lefschetz (1,1) theorem The Lefschetz (1,1) theorem revisited Formulation of the general Hodge conjecture Chern class theory
Mapping class group and a global Torelli theorem for hyperkähler manifolds
A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. In the published version of "Mapping class group and a global Torelli theorem for hyperkahler
On the Picard-Lefschetz transformation for algebraic manifolds acquiring general singularities
We consider a holomorphic family IvtitED of projective algebraic varieties Vt parametrized by the unit disc D {t e C: |ti < 1f and where Vt is smooth for t 0 but V0 may have arbitrary singularities.
Discrete Subgroups of Semisimple Lie Groups
1. Statement of Main Results.- 2. Synopsis of the Chapters.- 3. Remarks on the Structure of the Book, References and Notation.- 1. Preliminaries.- 0. Notation, Terminology and Some Basic Facts.- 1.
...
...