Further Details

Title: Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck
Condition: New
Author: Jean-Michel Bismut, Shu Shen, Zhaoting Wei
Format: Hardback
Type: Hardback
EAN: 9783031272332
ISBN: 9783031272332
Edition: 1st ed. 2023
Publisher: Birkhauser Verlag AG
Genre: Science Nature & Math
Release Date: 14/11/2023
Language: English
Country/Region of Manufacture: CH
Item Height: 235mm
Item Length: 155mm
Book Series: Progress in Mathematics
Release Year: 2023
Description: This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck  theorem.  One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections.  Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian.
Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource formany researchers in geometry, analysis, and mathematical physics. 

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