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Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck

BuchGebunden
184 Seiten
Englisch
Springererschienen am14.11.20231st ed. 2023
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.mehr
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BuchGebunden
EUR128,39
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Produkt

KlappentextThis 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.
Details
ISBN/GTIN978-3-031-27233-2
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2023
Erscheinungsdatum14.11.2023
Auflage1st ed. 2023
ReiheProgress in Mathematics
Seiten184 Seiten
SpracheEnglisch
IllustrationenX, 184 p. 1 illus.
Artikel-Nr.51986914

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr

Autor

Jean-Michel Bismut is a French mathematician who is a professor in the Mathematics Department in Orsay. He is known for his contributions to index theory, geometric analysis and probability theory. Together with Gilles Lebeau, he has developed the theory of the hypoelliptic Laplacian, to which he found applications in various fields of mathematics. He shared the Shaw Prize in Mathematical Sciences 2021 with Jeff Cheeger.
Shu Shen is a maître de conférences at Sorbonne University in Paris. His research focuses on the fields of analysis, geometry, and representation theory.
Zhaoting Wei is an assistant professor in mathematics at Texas A&M University-Commerce, USA. His research interests include noncommutative geometry and higher category theory.
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