Autour de la cohomologie de Bott-Chern

By M. Schweitzer. 2007

116 citations recorded by the source corpus.

The goal of the memoir is to develop a new cohomology theory which encompasses De Rham and Dolbeault cohomology as well as Deligne Beilinson cohomology, in the context of general complex analytic manifolds. The special case of the Iwasawa manifold is investigated as a typical example of what occurs in the non K\"ahler case. Elementary applications to the Kodaira-Spencer deformation theory and to the calculation of Chern classes are given.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4fd6950ad975866dbec6f30091c82ac18c5953ca

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Valentino Tosatti
2. B. Weinkove
3. Xiaokui Yang
4. G'abor Sz'ekelyhidi
5. Duong H. Phong
6. Dat T. To
7. M. Gill
8. Jianchun Chu

In Mathematical Physics

1. Valentino Tosatti
2. B. Weinkove
3. Duong H. Phong

Citations in the corpus

• The Chern–Ricci flow on complex surfaces (2012, background): “mensional real vector spaces, and when n = 2 they are isomorphic. In fact, H1,1 BC(M,R) ∼= H 1,1 A (M,R)∗ through the pairing H1,1 BC(M,R) × H 1,1 A (M,R) → R given by wedge and integration (see e.g. [42]). First of all recall a few facts from [17, pp.737-738]: the Bott-Chern cohomology group H1,1 B”
• Cohomology and Hodge Theory on Symplectic Manifolds: III (2009, unknown): “r the pair Hk d+dΛ(M) and H k ddΛ(M) defined on symplectic manifold. Indeed, both can be shown to be finite dimensional by constructing self-adjoint fourth-order differential operators [14, 3] (see also [20]). Explicitly, the fourth-order operators are DBC = (∂∂¯)(∂¯∗∂∗) +(∂¯∗∂∗)(∂∂¯)+(∂∗∂¯)(∂¯∗∂) +(∂¯”