scholarly journals Logarithmic Hodge structures and classifying spaces

2000 ◽  
pp. 115-130 ◽  
Author(s):  
Kazuya Kato ◽  
Sampei Usui
Keyword(s):  
Classifying Spaces ◽  
Hodge Structures

scholarly journals Classifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagram

2018 ◽  
Vol 58 (2) ◽  
pp. 289-426
Author(s):  
Kazuya Kato ◽  
Chikara Nakayama ◽  
Sampei Usui
Keyword(s):  
Classifying Spaces ◽  
Fundamental Diagram ◽  
Hodge Structures ◽  
Mixed Hodge Structures

scholarly journals Classifying spaces of degenerating mixed Hodge structures, II: Spaces of $\operatorname{SL}(2)$ -orbits

2011 ◽  
Vol 51 (1) ◽  
pp. 149-261 ◽  
Author(s):  
Kazuya Kato ◽  
Chikara Nakayama ◽  
Sampei Usui
Keyword(s):  
Classifying Spaces ◽  
Hodge Structures ◽  
Mixed Hodge Structures

Introduction to Variations of Hodge Structure

2017 ◽  
Author(s):  
Eduardo Cattani
Keyword(s):  
Asymptotic Behavior ◽  
Hodge Structure ◽  
Flat Connection ◽  
Classifying Spaces ◽  
Hodge Structures ◽  
Projective Varieties ◽  
Local Systems ◽  
Period Mapping ◽  
Variations Of Hodge Structure ◽  
Smooth Projective Varieties

This chapter emphasizes the theory of abstract variations of Hodge structure (VHS) and, in particular, their asymptotic behavior. It first studies the basic correspondence between local systems, representations of the fundamental group, and bundles with a flat connection. The chapter then turns to analytic families of smooth projective varieties, the Kodaira–Spencer map, Griffiths' period map, and a discussion of its main properties: holomorphicity and horizontality. These properties motivate the notion of an abstract VHS. Next, the chapter defines the classifying spaces for polarized Hodge structures and studies some of their basic properties. Finally, the chapter deals with the asymptotics of a period mapping with particular attention to Schmid's orbit theorems.

Characteristic classes for the classifying spaces of hodge structures

K-Theory ◽  
1987 ◽  
Vol 1 (3) ◽  
pp. 237-270 ◽  
Author(s):  
Ruth Charney ◽  
Ronnie Lee
Keyword(s):  
Characteristic Classes ◽  
Classifying Spaces ◽  
Hodge Structures

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

2017 ◽  
Author(s):  
Claire Voisin
Keyword(s):  
Recent Work ◽  
Chow Groups ◽  
Ring Structure ◽  
Complete Intersections ◽  
Algebraic Varieties ◽  
Chow Ring ◽  
Hodge Structures ◽  
Chow Rings ◽  
Geometric Methods ◽  
The Right

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The book is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by the author. It focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by the author looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.

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