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Birkhauser Coherent Sheaves and Riemann-Roch-Grothendieck 347

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Description

This monograph from Birkhauser explores two major questions in complex geometry. It focuses on the construction of a Chern character on the Grothendieck group of coherent sheaves for a compact complex manifold, specifically with values in its Bott-Chern cohomology. The text also provides a proof for a corresponding Riemann-Roch-Grothendieck theorem. As part of the Progress in Mathematics series, volume 347 utilizes the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Through Chern-Weil theoretic techniques, the work constructs forms that represent the Chern character, providing a deep mathematical foundation for researchers in algebra and complex geometry.

Key Features

This Birkhauser monograph addresses complex geometry questions regarding the construction of a Chern character.

The text provides a detailed proof of a corresponding Riemann-Roch-Grothendieck theorem.

It utilizes the Block equivalence of categories between derived categories and the homotopy category of antiholomorphic superconnections.

Chern-Weil theoretic techniques are applied to construct forms that represent the Chern character.

This volume is part of the Progress in Mathematics series, specifically number 347.

Product Specifications

Format
hardcover
Domain
Amazon UK
Release Date
14 November 2023
Listed Since
25 January 2023

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