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...
محفوظ في:
| المؤلفون الرئيسيون: | , , |
|---|---|
| مؤلف مشترك: | |
| التنسيق: | الكتروني كتاب الكتروني |
| اللغة: | الإنجليزية |
| منشور في: |
Cham :
Springer International Publishing : Imprint: Birkhäuser,
2023.
|
| الطبعة: | 1st ed. 2023. |
| سلاسل: | Progress in Mathematics,
347 |
| الموضوعات: | |
| الوصول للمادة أونلاين: | https://doi.org/10.1007/978-3-031-27234-9 |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
| الملخص: | 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 manyresearchers in geometry, analysis, and mathematical physics. . |
|---|---|
| وصف مادي: | X, 184 p. 1 illus. online resource. |
| ردمك: | 9783031272349 |
| تدمد: | 2296-505X ; |
| DOI: | 10.1007/978-3-031-27234-9 |