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On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety
Author: Mark Green

ISBN: 9780691120447
Format: Paperback
Number Of Pages: 208
Published: 5 December 2004
Country of Publication: US
Dimensions (cm): 22.9 x 15.2 x 1.1
Description:


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 interesti...

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