arXiv subjects

Crislaine Kuster

Publications and source records attributed to Crislaine Kuster.

4 recordsLinked to original sources

arXiv2026

Minimal-Degree Foliations on Cominuscule Grassmannians

Given $X$ a cominuscule Grassmannian (or irreducible Hermitian symmetric space) and an integer $p,$ we compute the minimum $l(p)$ such that $H^0 (Ω^p_X (l(p)))$ is not 0. This allows us to conclude that any codimension-one foliation of degree zero on a cominuscule Grassmannian is a pencil of hyperplanes, improving a result of the first and third authors with D. Faenzi. We also deduce the structure of codimension-one foliations of degree one. Finally, we provide families of examples of high codimensional foliations of minimal degree on classical Grassmannians, Lagrangian Grassmannians, Spinor varieties, and the Cayley plane.

math.AG↗

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↗

arXiv2025

Codimension-one foliations on adjoint varieties

In this paper, we classify codimension-one foliations on adjoint varieties with most positive anti-canonical class. On adjoint varieties of Picard number one, we show that such foliations are always induced by a pencil of hyperplane sections with respect to the minimal embedding. For adjoint varieties of Picard number two, we prove that the space of such foliations contains more than one irreducible component, and we describe each of them. As a tool for understanding these foliations, we introduce the concept of the degree of a foliation with respect to a family of rational curves, which may be of independent interest.

math.AG↗

arXiv2023

The algebraic and geometric classification of antiassociative algebras

This paper is devoted to the complete algebraic and geometric classification of complex 4 and 5-dimensional antiassociative algebras. In particular, we proved that the variety of complex 4-dimensional antiassociative algebras has dimension 12 and it is defined by three irreducible components (in particular, there is only 1 rigid algebra in this variety); the variety of complex 5-dimensional antiassociative algebras has dimension 24 and it is defined by 8 irreducible components (in particular, there are only 4 rigid algebras in this variety).

math.RA↗