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Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck
Hardcover
Series: Progress in Mathematics, Book 347
AlgebraGeneral MathematicsGeometry
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ISBN10: 3031272331
ISBN13: 9783031272332
Publisher: Birkhauser
Published: Nov 14 2023
Pages: 184
Weight: 1.00
Height: 0.50 Width: 6.14 Depth: 9.21
Language: English
ISBN13: 9783031272332
Publisher: Birkhauser
Published: Nov 14 2023
Pages: 184
Weight: 1.00
Height: 0.50 Width: 6.14 Depth: 9.21
Language: English
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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