Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck PDF
by Jean-Michel Bismut, Shu Shen, Zhaoting Wei
Part of the Progress in Mathematics series
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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.
Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer International Publishing
- Publication Date:13/11/2023
- Category:
- ISBN:9783031272349
Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer International Publishing
- Publication Date:13/11/2023
- Category:
- ISBN:9783031272349
