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Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck/ by Jean-Michel Bismut, Shu Shen, Zhaoting Wei.
作者:	Bismut, Jean-Michel.
其他作者:	Wei, Zhaoting.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	x, 184 p. :illustrations, digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Differential Geometry. -
電子資源:	https://doi.org/10.1007/978-3-031-27234-9
ISBN:	9783031272349

Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck
Bismut, Jean-Michel.

Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck[electronic resource] /by Jean-Michel Bismut, Shu Shen, Zhaoting Wei. - Cham :Springer International Publishing :2023. - x, 184 p. :illustrations, digital ;24 cm. - Progress in mathematics,v. 3472296-505X ;. - Progress in mathematics ;v.231..

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 for many researchers in geometry, analysis, and mathematical physics.

ISBN: 9783031272349

Standard No.: 10.1007/978-3-031-27234-9doiSubjects--Topical Terms:

671118
Differential Geometry.

LC Class. No.: QA613.618

Dewey Class. No.: 516.183

Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck
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520 $a 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 for many researchers in geometry, analysis, and mathematical physics.
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