On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) (Annals of Mathematics Studies) (Annals of Mathematics Studies, 157) - Softcover
Book 8 of 202: Annals of Mathematics Studies
Synopsis
In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group. Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles.
The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups. Bloch's formula is motivated by algebraic K-theory and involves differentials over Q. The theory developed here is characterized by the appearance of arithmetic considerations even in the local infinitesimal theory of algebraic cycles. The map from the tangent space to the Hilbert scheme to the tangent space to algebraic cycles passes through a variant of an interesting construction in commutative algebra due to Angéniol and Lejeune-Jalabert. The link between the theory given here and Bloch's formula arises from an interpretation of the Cousin flasque resolution of differentials over Q as the tangent sequence to the Gersten resolution in algebraic K-theory. The case of 0-cycles on a surface is used for illustrative purposes to avoid undue technical complications.
"synopsis" may belong to another edition of this title.
About the Author
Mark Green is Professor of Mathematics and Director of the Institute for Pure and Applied Mathematics at the University of California, Los Angeles. Phillip Griffiths is Professor in the School of Mathematics at the Institute of Advanced Study.
"About this title" may belong to another edition of this title.
Other Popular Editions of the Same Title
Search results for On the Tangent Space to the Space of Algebraic Cycles...
Stock Image
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety (Annals of Mathematics Studies, 157)
Published by
Princeton University Press, 2005
ISBN 10: 0691120447
ISBN 13: 9780691120447
Used
paperback
Seller: Evergreen Goodwill, Seattle, WA, U.S.A.
Seller rating 5 out of 5 stars
paperback. Condition: Good. Seller Inventory # mon0000292635
Stock Image
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) (Annals of Mathematics Studies, 157)
Published by
Princeton University Press, 2005
ISBN 10: 0691120447
ISBN 13: 9780691120447
Used
Softcover
Seller: World of Books (was SecondSale), Montgomery, IL, U.S.A.
Seller rating 5 out of 5 stars
Condition: Good. Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc. Seller Inventory # 00021281916
Stock Image
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (Am-157) (Annals of Mathematics Studies)
Published by
Princeton University Press, 2005
ISBN 10: 0691120447
ISBN 13: 9780691120447
Used
Softcover
Seller: Anybook.com, Lincoln, United Kingdom
Seller rating 5 out of 5 stars
Condition: Good. This is an ex-library book and may have the usual library/used-book markings inside.This book has soft covers. In good all round condition. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,400grams, ISBN:9780691120447. Seller Inventory # 5832946
Buy Used
£ 17.20
Shipping:
£ 12.94
From United Kingdom to U.S.A.
Quantity: 1 available
Seller Image
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety
Seller: The Haunted Bookshop, LLC, Iowa City, IA, U.S.A.
Seller rating 5 out of 5 stars
Paperback. Condition: Fine. Crisp, clean pages; no owners' marks; as new. vi, 200pp. incl. index.; Annals of Mathematics Studies Series; Vol. 157. Seller Inventory # 80540
Stock Image
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) (Annals of Mathematics Studies) (Annals of Mathematics Studies (157))
Published by
Princeton University Press, 2005
ISBN 10: 0691120447
ISBN 13: 9780691120447
New
Softcover
Seller: Labyrinth Books, Princeton, NJ, U.S.A.
Seller rating 4 out of 5 stars
Condition: New. Seller Inventory # 127119
Stock Image
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. Annals of Mathematics Studies, 157.
Published by
Princeton University Press. 2005., 2005
ISBN 10: 0691120447
ISBN 13: 9780691120447
Used
Softcover
Seller: Antiquariaat Ovidius, Bredevoort, Netherlands
Seller rating 4 out of 5 stars
Condition: Gebraucht / Used. 45,00 EURO Paperback. Very good. Vi,200pp. Seller Inventory # 112569
Stock Image
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (Annals of Mathematics Studies, 157, Band 157).
Published by
Princeton University Press., 2005
ISBN 10: 0691120447
ISBN 13: 9780691120447
Used
kartoniert
Seller: Antiquariat Bernhardt, Kassel, Germany
Seller rating 5 out of 5 stars
kartoniert. Condition: Sehr gut. Zust: Gutes Exemplar. 200 Seiten, mit Abbildungen, Englisch 306g. Seller Inventory # 360395
Seller Image
On The Tangent Space To The Space Of Algebraic Cycles On A Smooth Algebraic Variety
Published by
Princeton University Press, 2005
ISBN 10: 0691120447
ISBN 13: 9780691120447
New
Softcover
Seller: GreatBookPrices, Columbia, MD, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # 2558118-n
Seller Image
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety
Published by
Princeton University Press, US, 2005
ISBN 10: 0691120447
ISBN 13: 9780691120447
New
Paperback
Seller: Rarewaves USA, OSWEGO, IL, U.S.A.
Seller rating 5 out of 5 stars
Paperback. Condition: New. In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group. Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles. The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups. Bloch's formula is motivated by algebraic K-theory and involves differentials over Q. The theory developed here is characterized by the appearance of arithmetic considerations even in the local infinitesimal theory of algebraic cycles. The map from the tangent space to the Hilbert scheme to the tangent space to algebraic cycles passes through a variant of an interesting construction in commutative algebra due to Angeniol and Lejeune-Jalabert.The link between the theory given here and Bloch's formula arises from an interpretation of the Cousin flasque resolution of differentials over Q as the tangent sequence to the Gersten resolution in algebraic K-theory. The case of 0-cycles on a surface is used for illustrative purposes to avoid undue technical complications. Seller Inventory # LU-9780691120447
Stock Image
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) (Annals of Mathematics Studies)
Print on DemandSeller: Revaluation Books, Exeter, United Kingdom
Seller rating 5 out of 5 stars
Paperback. Condition: Brand New. 200 pages. 9.00x6.25x0.75 inches. In Stock. This item is printed on demand. Seller Inventory # __0691120447