Chow Rings, Decomposition of the Diagonal, and the Topology of Families
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A01=Claire Voisin
Abelian category
Abelian variety
Algebraic cycle
Algebraic variety
Ample line bundle
Author_Claire Voisin
Birational invariant
Category=PBCH
Category=PBG
Category=PBPD
Chow group
Codimension
Coefficient
Cohomology
Cohomology ring
Collinearity
Commutative diagram
Complete intersection
Complex cobordism
Complex differential form
Conjecture
Conjugacy class
Countable set
Dense set
Derived category
Diagonal
Differentiable function
Differential geometry of surfaces
Dimension (vector space)
Direct sum
Division by zero
Divisor
Elliptic curve
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exact sequence
Existential quantification
Fiber bundle
Fibration
Generic point
Hodge conjecture
Hodge structure
Hodge theory
Homology (mathematics)
Hypersurface
Integer
Intersection form (4-manifold)
Irreducible component
Leray spectral sequence
Line bundle
Moduli space
Morphism
Natural transformation
Norm residue isomorphism theorem
Normal bundle
Open set
Parametrization
Permutation
Polynomial
Projective space
Projective variety
Quadric
Rational variety
Resolution of singularities
Sheaf (mathematics)
Subgroup
Subset
Summation
Tensor product
Theorem
Topology
Torsor (algebraic geometry)
Variable (mathematics)
Vector bundle
Zariski topology
Zero set
Product details
- ISBN 9780691160511
- Weight: 28g
- Dimensions: 152 x 235mm
- Publication Date: 23 Feb 2014
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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-Kahler manifolds.
In particular, the book delves into arguments originating in Nori's work that have been further developed by others.
Claire Voisin has been a senior researcher at France's National Center for Scientific Research since 1986.
