Hodge Structures and Homological Methods

2012 ◽  
pp. 203-221
Author(s):  
Donu Arapura
Keyword(s):  
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.

scholarly journals On the boundary of the moduli spaces of log Hodge structures: Triviality of the torsor

2010 ◽  
Vol 198 ◽  
pp. 173-190 ◽  
Author(s):  
Tatsuki Hayama
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Hodge Structures

AbstractThis paper examines the moduli spaces of log Hodge structures introduced by Kato and Usui. This moduli space is a partial compactification of a discrete quotient of a period domain. This paper treats the following two cases: (A) where the period domain is Hermitian symmetric, and (B) where the Hodge structures are of the mirror quintic type. Especially it addresses a property of the torsor.

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