Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck
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 theor...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Birkhäuser
2023, 2023
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| Edition: | 1st ed. 2023 |
| Series: | Progress in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Introduction
- Bott-Chern Cohomology and Characteristic Classes
- The Derived Category ${\mathrm{D {b}_{\mathrm{coh}}}}$
- Preliminaries on Linear Algebra and Differential Geometry
- The Antiholomorphic Superconnections of Block
- An Equivalence of Categories
- Antiholomorphic Superconnections and Generalized Metrics
- Generalized Metrics and Chern Character Forms
- The Case of Embeddings
- Submersions and Elliptic Superconnections
- Elliptic Superconnection Forms and Direct Images
- A Proof of Theorem 10-1 when $\overline{\partial} {X}\partial {X}\omega {X}=0$.
- The Hypoelliptic Superconnections
- The Hypoelliptic Superconnection Forms
- The Hypoelliptic Superconnection Forms when $\overline{\partial} {X}\partial {X}\omega {X}=0$
- Exotic Superconnections and Riemann-Roch-Grothendieck
- Subject Index
- Index of Notation
- Bibliography