arXiv subjects

P. Rubí Pantaleón-Mondragón

Publications and source records attributed to P. Rubí Pantaleón-Mondragón.

4 recordsLinked to original sources

arXiv2026

Initial Ideals, Low-degree Foliations and the Hilbert Scheme of Points on $\mathbb{CP}^{2}$: A First Approach

The holomorphic foliations of degree $d$ on $\mathbb{CP}^{2}$ with isolated singularities are determined by their singular subschemes, which correspond to elements in the Hilbert Scheme of $N=d^{2}+d+1$ points. In this paper, we analyze the affine varieties parametrized by a partition of $N=7$ that cover the Hilbert Scheme of seven points, with the property that the Hilbert function of the elements in these affine varieties corresponds to that of holomorphic foliation of degree $d=2$. Moreover, we present some results for degree $3$.

math.AG↗

arXiv2026

Projective Foliations with a Unique Singular Point and Maximum Algebraic Multiplicity

The study of codimension-one holomorphic foliations on the projective plane $\mathbb{CP}^{2}$ with a unique singular point has attracted increasing interest because of its connections with several important problems. In this paper, we focus on holomorphic foliations of degree $d$ having a singular point of maximal multiplicity $d$. We describe explicitly the foliations in this class and characterize those having a unique singular point. We also state some results concerning Hilbert-Mumford stability for these foliations.

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arXiv2023

On the stability of foliations of degree 3 with a unique singular point

Applying Geometric Invariant Theory (GIT), we study the stability of foliations of degree 3 on P^2 with a unique singular point of multiplicity 1, 2, or 3 and Milnor number 13. In particular, we characterize those foliations for multiplicity 2 in three cases: stable, strictly semistable, and unstable.

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arXiv2023

The Euler-Betti Algorithm to identify foliations in Hilbert Scheme

Foliations in the complex projective plane are uniquely determined by their singular locus, which is in correspondence with a zero-dimensional ideal. However, this correspondence is not surjective. We give conditions to determine whether an ideal arises as the singular locus of a foliation or not. Furthermore, we give an effective method to construct the foliation in the positive case.

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