3 papers
math.AG2025
A primer on measures of irrationality
Nathan Chen, Olivier Martin
Measures of irrationality are a numerical way of quantifying how far a given variety is from being rational (or rationally connected, uniruled, etc.). In the last two decades, ther…
math.AG2025
Low degree subvarieties of universal hypersurfaces
Yifeng Huang, Borys Kadets, Olivier Martin
We study irreducible subvarieties of the universal hypersurface of degree and dimension . We prove that when is sufficiently large, a degree subvari…
math.AG2023
Isotrivial Lagrangian fibrations of compact hyper-Kähler manifolds
Yoon-Joo Kim, Radu Laza, Olivier Martin
This article initiates the study of isotrivial Lagrangian fibrations of compact hyper-Kähler manifolds. We present four foundational results that extend well-known facts about isot…