3 papers
math.AG2026
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.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.AG2024
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 iso…