Topological and arithmetic characteristics about products of projective lines with complex tori
Abstract
In this paper, we study non-planar degeneracies with cylindrical configurations. They could be constructed by the product $\mathbb{CP}^1 \times T$ of the projective plane and a complex torus with embedding $(m,n)$. We prove that their fundamental groups of Galois covers have an abelian subgroup of rank $m(2n-1)$ respectively, and the irregularity of these surfaces are at least $2mn-1$. Furthermore, we also use Chern numbers to compute the index of such surfaces and classify them.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Geometric and Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 16 February 2026
- Language
- EN
- Document type
- Preprint