Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck

Anglický jazyk

Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck

Vydavateľstvo: Springer International Publishing
Rok vydania: 2024
Formát: Paperback
Rozmer: 235 x 155 mm
Jazyk: Anglický jazyk
ISBN: 9783031272363

Na objednávku

118.79 €

bežná cena: 131.99 €

O knihe

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.