Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck (Progress in Mathematics #347) (Hardcover)

Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck (Progress in Mathematics #347) By Jean-Michel Bismut, Shu Shen, Zhaoting Wei Cover Image
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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.
Product Details
ISBN: 9783031272332
ISBN-10: 3031272331
Publisher: Birkhauser
Publication Date: November 14th, 2023
Pages: 184
Language: English
Series: Progress in Mathematics