Atiyah classes with values in the truncated cotangent complex
Fabian Langholf

TL;DR
This paper derives an explicit formula for the truncated Atiyah class of complexes of vector bundles and shows the first truncated Chern class depends solely on the determinant.
Contribution
It provides a new explicit formula for the truncated Atiyah class and clarifies the dependence of the first truncated Chern class on the determinant.
Findings
Explicit formula for the truncated Atiyah class
First truncated Chern class depends only on the determinant
Enhanced understanding of vector bundle complexes
Abstract
We prove an explicit formula for the truncated Atiyah class of a bounded complex of vector bundles. Furthermore, we show that the first truncated Chern class of such a complex only depends on its determinant.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds
