Topological complexity of enumerative problems and classifying spaces of PUn
Abstract
Abstract We study the topological complexity, in the sense of Smale, of three enumerative problems in algebraic geometry: finding the 27 lines on cubic surfaces, the 28 bitangents and the 24 inflection points on quartic curves. In particular, we prove lower bounds for the topological complexity of any algorithm that finds solution to the three problems and for the Schwarz genera of their associated covers. The key is to understand cohomology classes of the classifying spaces of projective unitary groups .
Fields of Study & Subjects
Coding theory and cryptography
graph theory and CDMA systems
Digital Image Processing Techniques
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 6
- Publication date
- 1 June 2026
- Language
- EN