English

What makes an algebraic curve special?

Algebraic Geometry 2025-02-11 v1 Number Theory

Abstract

A survey of special curves, special subvarieties of Mg\mathcal{M}_g, and related topics. A large portion of the text discusses various possible interpretation of the word 'special' in this context by giving also concrete examples. One highlight is the bi-algebraic viewpoint for atypical intersections appearing in Hodge theory as well as, more recently, in Teichm\"{u}ller theory.

Keywords

Cite

@article{arxiv.2502.06366,
  title  = {What makes an algebraic curve special?},
  author = {Gregorio Baldi},
  journal= {arXiv preprint arXiv:2502.06366},
  year   = {2025}
}

Comments

First version, comments are welcome!

R2 v1 2026-06-28T21:38:25.879Z