Description 
1 online resource (vi, 200 pages) : illustrations 
Series 
Annals of mathematics studies ; no. 157 

Annals of mathematics studies ; no. 157.

Contents 
Frontmatter  Contents  Abstract  Chapter One. Introduction  Chapter Two. The Classical Case When n 1  Chapter Three. Differential Geometry of Symmetric Products  Chapter Four. Absolute Differentials (I)  Chapter Five Geometric Description of T̳Z  Chapter Six. Absolute Differentials (II)  Chapter Seven. The Extdefinition of TZ  Chapter Eight. Tangents to Related Spaces  Chapter Nine. Applications and Examples  Chapter Ten. Speculations and Questions  Bibliography  Index 
Summary 
In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodgetheoretic constructions such as the cycle class and the AbelJacobi 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 Ktheory 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 LejeuneJalabert. 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 Ktheory. The case of 0cycles on a surface is used for illustrative purposes to avoid undue technical complications 
Bibliography 
Includes bibliographical references (pages 195197) and index 
Notes 
In English 

Print version record 
Subject 
Algebraic cycles.


Geometry, Algebraic.


Hodge theory.


MATHEMATICS  Geometry  Algebraic.


MATHEMATICS  Algebra  Abstract.


Algebraic cycles.


Geometry, Algebraic.


Hodge theory.

Form 
Electronic book

ISBN 
9780691120430 

0691120439 

9781400837175 

1400837170 
