Titlebook: Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck; Jean-Michel Bismut,Shu Shen,Zhaoting Wei Book 2023 The Editor(s) (if ap

装入胶囊

Tommaso Polonelli,Michele MagnoWe describe the main results contained in the book. In particular, if . is a compact complex manifold, we outline the construction of the Chern character of coherent sheaves with values in Bott-Chern cohomology, we state the corresponding Riemann-Roch-Grothendieck theorem, and we give a sketch of the proof.

鸽子

礼节

epicondylitis

Francisco Martins,Luís Lopes,Hervé PaulinoWe recall elementary facts of linear algebra and differential geometry, in particular on connections on a real tangent bundle with nonzero torsion.

deadlock

Dulce Domingos,Francisco Martins,Lara CaiolaWe recall the definition of the antiholomorphic superconnections of Block, and we study their functorial properties. We prove that the associated sheaf cohomology is coherent, and we show that the corresponding determinant is a holomorphic line bundle.

farewell

追踪

Intractable

Macronutrients

https://doi.org/10.1007/978-3-642-23583-2We establish the Riemann-Roch-Grothendieck theorem in the case of embeddings.

vector

Hervé Paulino,João Ruivo SantosWe state the Riemann-Roch-Grothendieck theorem in the case of a projection .. Given metric data, we construct an infinite-dimensional antiholomorphic superconnection with fiberwise elliptic curvature, and we obtain corresponding Chern character forms on ., whose Bott-Chern class does not depend on the metrics.