Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck (1st ed. 2023)

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 for many researchers in geometry, analysis, and mathematical physics. 

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Progress in Mathematics, 347
Release date:	September 2023
Authors:	Jean-Michel Bismut • Shu Shen • Zhaoting Wei
Dimensions:	235 x 155mm (L x W)
Pages:	188
Edition:	1st ed. 2023
ISBN-13:	978-3-03-127233-2
Categories:	Books
LSN:	3-03-127233-1
Barcode:	9783031272332

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