Coherent Sheaves, Superconnections and Riemann-roch-grothendieck
Book Details
Format
Paperback / Softback
Book Series
Progress in Mathematics
ISBN-10
3031272366
ISBN-13
9783031272363
Publisher
Birkhauser Verlag AG
Imprint
Birkhauser Verlag AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Nov 14th, 2024
Print length
184 Pages
Ksh 19,800.00
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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.
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.
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