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...
Gorde:
| Egile Nagusiak: | , , |
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| Erakunde egilea: | |
| Formatua: | Baliabide elektronikoa eBook |
| Hizkuntza: | ingelesa |
| Argitaratua: |
Cham :
Springer International Publishing : Imprint: Birkhäuser,
2023.
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| Edizioa: | 1st ed. 2023. |
| Saila: | Progress in Mathematics,
347 |
| Gaiak: | |
| Sarrera elektronikoa: | https://doi.org/10.1007/978-3-031-27234-9 |
| Etiketak: |
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Aurkibidea:
- 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.