The FRACASSO project aims to achieve a deeper understanding of rational connectedness on Fano varieties, which are key objects in the field of algebraic geometry. The main objective of the project is to study a recent refined version of rational connectedness, known as rational simple connectedness, and its arithmetic consequences on the geometry of rational points. This notion was introduced by de Jong and Starr and involves the rational connectedness of moduli spaces of rational curves.

Fano varieties are an important class of algebraic varieties, playing a key role in the birational classification of these objects. This project aims to explore algebro-geometric and arithmetic implications of rational simple connectedness for Fano varieties.

The Fracasso project consists of three main axes:

  1. Geometric FRACASSO, to explore the geometry of moduli spaces of rational curves.
  2. Numerical FRACASSO, to investigate other notions of higher Fano varieties.
  3. Arithmetic FRACASSO, to study rational points on rationally simply connected varieties.