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On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) (Paperback, New) Loot Price: R1,751
Discovery Miles 17 510
You Save: R100 (5%)
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) (Paperback, New): Mark Green,...

On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) (Paperback, New)

Mark Green, Phillip A. Griffiths

Series: Annals of Mathematics Studies

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List price R1,851 Loot Price R1,751 Discovery Miles 17 510 | Repayment Terms: R164 pm x 12* You Save R100 (5%)

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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."

General

Imprint: Princeton University Press
Country of origin: United States
Series: Annals of Mathematics Studies
Release date: 2005
First published: 2005
Authors: Mark Green • Phillip A. Griffiths
Dimensions: 235 x 152 x 18mm (L x W x T)
Format: Paperback - Trade
Pages: 208
Edition: New
ISBN-13: 978-0-691-12044-7
Categories: Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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LSN: 0-691-12044-7
Barcode: 9780691120447

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