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Ruben Lizarbe

Publications and source records attributed to Ruben Lizarbe.

5 recordsLinked to original sources
arXiv2025

Degree-one foliations on complete intersections

We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for any smooth hypersurface of dimension at least three that is not a quadric threefold. The proof of these results follows essentially from a more general structure theorem for foliations on manifolds covered by lines.

math.AG↗
arXiv2022

Affine connections on complex compact surfaces and Riccati distributions

Let $M$ be a complex surface. We show that there is a one-to-one correspondence between torsion-free affine connections on $M$ and Riccati distributions on $\mathbb{P}(TM)$. Furthermore, if $M$ is compact, then this correspondence induces a one-to-one correspondence between affine structures on $M$ and Riccati foliations on $\mathbb{P}(TM)$.

math.DG↗
arXiv2021

Codimension one foliations of degree three on projective spaces

We establish a structure theorem for degree three codimension one foliations on projective spaces of dimension $n\ge 3$, extending a result by Loray, Pereira, and Touzet for degree three foliations on $\mathbb P^3$. We show that the space of codimension one foliations of degree three on $\mathbb{P}^n$, $n\ge 3$, has exactly $18$ distinct irreducible components parameterizing foliations without rational first integrals, and at least $6$ distinct irreducible components parameterizing foliations with rational first integrals.

math.AG↗