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Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck

Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck

Jean-Michel Bismut, Shu Shen, Zhaoting Wei

Birkhäuser
Collection: Progress in Mathematics
Publication date : 2023-11-13

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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. 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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About the book

Author

Jean-Michel Bismut , Shu Shen , Zhaoting Wei

Imprint

Birkhäuser

Collection

Progress in Mathematics

Publication date

2023-11-13

Pages

184 pages

Print ISBN

9783031272332

Language

English

Ebook informations

EAN PDF

9783031272349

Price

£109.99

Copy count 1

Print count 18

File size 2437 Ko

Informations accessibility

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About author(s)

Jean-Michel Bismut

Shu Shen

Zhaoting Wei

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