On the degree of a modular map

Ciro Ciliberto; Alessandro verra

On the degree of a modular map

Algebraic Geometry 2024-09-20 v1

Authors: Ciro Ciliberto , Alessandro verra

Abstract

Let $X$ be a general cubic hypersurface in $\mathbb P^4$ . If $x\in X$ is a general point there are exactly six distinct lines in $X$ passing through $x$ , that lie on the rank 3 quadric cone with vertex $x$ of lines that have intersection multiplicity at least 3 with $X$ in $x$ . So there is a natural rational map $X\dasharrow \mathcal M_2$ . In this paper we compute its degree to be 2074320.

Keywords

cubic fourfolds rational points on curves rational maps

Cite

@article{arxiv.2409.12542,
  title  = {On the degree of a modular map},
  author = {Ciro Ciliberto and Alessandro verra},
  journal= {arXiv preprint arXiv:2409.12542},
  year   = {2024}
}