This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.

Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics)

Science & Math

Voisin, Claire

Mathematics

Cambridge University Press

A modern introduction to Kaehlerian geometry and Hodge structure written for students.

Hodge Theory and Complex Algebraic Geometry I ICM Edition: Volume 1 (Cambridge Studies in Advanced Mathematics, Series Number 76)

Hodge Theory and Complex Algebraic Geometry II ICM Edition: Volume 2 (Cambridge Studies in Advanced Mathematics, Series Number 77)

Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics, Series Number 76)

This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.

Hodge Theory and Complex Algebraic Geometry II: Volume 2 (Cambridge Studies in Advanced Mathematics, Series Number 77)

The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly, Nori's connectivity theorem, which generalizes the above. The last part deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry. Also available: Volume I 0-521-80260-1 Hardback $60.00 C

Reference

Foreign Language Study & Reference

The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly, Nori's connectivity theorem, which generalizes the above. The last part deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry. Also available: Volume I 0-521-80260-1 Hardback $60.00 C

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.

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

Princeton University Press

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (Annals of Mathematics Studies)

Although the majority of the world's Herons live in the tropics and subtropics, Europe is home to nine species, some large, some small, some colonial, some solitary breeders. Highly specialized birds, they exhibit many interesting differences in their behavior and ecology and are a favorite group for many ornithologists. Dr. Voisin begins her book with a general description of the family before going on to treat each species in more detail. The species accounts summarize such topics as field characters, distribution, population size, breeding, and feeding ecology and behavior. Numerous figures and tables are accompanied by fine drawings of behavior by P.L. Suiro and color and black and white pictures of each species by G. Brusewitz. Key Features* Full coverage of all European heron species* General chapters on basic heron biology* Color plates showing all species* Numerous line drawings, diagrams, and maps

The Herons of Europe (T & AD Poyser)

Biological Sciences

Academic Press

See the best price to sell, buy, or rent books by Voisin, Claire. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Voisin, Claire

See the best price to sell, buy, or rent books by Voisin, Claire. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics)

Hodge Theory and Complex Algebraic Geometry I ICM Edition: Volume 1 (Cambridge Studies in Advanced Mathematics, Series Number 76)

Hodge Theory and Complex Algebraic Geometry II ICM Edition: Volume 2 (Cambridge Studies in Advanced Mathematics, Series Number 77)

Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics, Series Number 76)

Hodge Theory and Complex Algebraic Geometry II: Volume 2 (Cambridge Studies in Advanced Mathematics, Series Number 77)

Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics, Series Number 76)

Hodge Theory and Complex Algebraic Geometry II: Volume 2 (Cambridge Studies in Advanced Mathematics, Series Number 77)

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

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (Annals of Mathematics Studies)

The Herons of Europe (T & AD Poyser)