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



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Autore: Voisin Claire Visualizza persona
Titolo: Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187) / / Claire Voisin Visualizza cluster
Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2014]
©2014
Edizione: Course Book
Descrizione fisica: 1 online resource (172 p.)
Disciplina: 516.35
Soggetto topico: Algebraic varieties
Decomposition (Mathematics)
Homology theory
Mathematics
Soggetto non controllato: Bloch-Beilinson conjectures
CalabiЙau hypersurfaces
Chow groups
Hodge classes
Hodge coniveau
Hodge structures
K3 surfaces
Lefschetz standard conjecture
Mumford's theorem
Z-coefficients
abelian varieties
birational invariants
cohomology
complex algebraic varieties
coniveau
cycle classes
decomposition isomorphism
decomposition
dense Zariski open set
diagonal
functoriality
generalized Bloch conjecture
generalized Hodge conjecture
geometric coniveau
hyper-Khler manifolds
integral coefficients
integral cohomological decomposition
mixed Hodge structures
projective space
rational equivalence
small diagonal
smooth projective varieties
spreading principle
torsion coefficients
transcendental cohomology
unramified cohomology
variety
Classificazione: SI 830
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Front matter -- Contents -- Preface -- Chapter One. Introduction -- Chapter Two. Review of Hodge theory and algebraic cycles -- Chapter Three. Decomposition of the diagonal -- Chapter Four. Chow groups of large coniveau complete intersections -- Chapter Five. On the Chow ring of K3 surfaces and hyper-Kähler manifolds -- Chapter Six. Integral coefficients -- Bibliography -- Index
Sommario/riassunto: In this book, Claire Voisin 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 volume 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 Voisin. The book 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 Voisin 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.
Titolo autorizzato: Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)  Visualizza cluster
ISBN: 1-4008-5053-3
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910790854503321
Lo trovi qui: Univ. Federico II
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Serie: Annals of Mathematics Studies