WebAug 20, 2009 · We give a universal approach to the deformation-obstruction theory of objects of the derived category of coherent sheaves over a smooth projective family. We recover and generalise the obstruction class of Lowen and Lieblich, and prove that it is a product of Atiyah and Kodaira–Spencer classes. This allows us to obtain deformation … WebNov 8, 2024 · An Atiyah class in the cohomology is the image under a natural linear injection of the contraction of a (constant) vector in \mathbb {C}^ {3} with the curvature F_ {A}^ {0}. We define the essential obstruction as the finite dimensional quotient
algebraic geometry - On the definition of the Atiyah class ...
WebOct 9, 2008 · We develop a formalism involving Atiyah classes of sheaves on a smooth manifold, Hochschild chain and cochain complexes. As an application we prove a version of the Riemann–Roch theorem. The Atiyah class, Hochschild cohomology and the Riemann–Roch theorem - Markarian - 2009 - Journal of the London Mathematical … Web(1.1.2) known as the Atiyah class of E An equivalent way of getting E is as follows. Let Conn ( E ) be the sheaf on X whose sections over U are holomorphic connections in E j U As well known, the space of such connections is an affine space over ( U; 1End E )) , so Conn isasheafof -torsors. Sheavesof torsors overany sheaf A pop in india
Rozansky–Witten invariants via Atiyah classes
Webthe Atiyah class and the Todd class [13] of this DG manifold. Meanwhile, (T KM;F) is a Lie algebroid pair over M. We may also consider the Atiyah class and the Todd class [3] of the Lie pair (T KM;F). The main purpose of this paper is to investigate the relation between these two types of Atiyah classes and Todd classes. WebSep 14, 2024 · On the definition of the Atiyah class. I am reading the book Complex Geometry: an Introduction by Daniel Huybrechts. On page 180 the author defined the … WebAtiyah–Jones conjecture it would now suffice to show that the maps tk in-duce isomorphism in homology and homotopy through a range. In 1993, Boyer, Hurtubise, Milgram and Mann [BHMM] proved that the Atiyah–Jones conjecture holds for the sphere S4 and in 1995, Hurtubise and Mann [HM] proved that the conjecture is true for ruled surfaces. pop in indiana