arXiv subjects

Aislan Fontes

Publications and source records attributed to Aislan Fontes.

3 recordsLinked to original sources

arXiv2026

New irreducible components of $\mathcal{B}(0,c_2)$ and Computation of the Dimension of its tangent space

We provide a Macaulay2 code for computing the dimension of the tangent space to $\mathcal{B}(e,c_2)$ in certain cases. Using this code, we identify components of $\mathcal{B}(e,c_2)$ containing singular points and compute the dimension of the irreducible component $M_4$ of $\mathcal{B}(-1,6)$, whose existence was proved in \cite{MF2021}. Furthermore, we prove the existence of infinite families of irreducible components of $\mathcal{B}(0,c_2)$.

math.AG↗

arXiv2024

Classification of monads and moduli components of stable rank 2 bundles with odd determinant and $c_2=10$

In this paper, we provide a complete classification of the positive minimal monads whose cohomology is a stable rank 2 bundle on $\mathbb{P}^3$ with Chern classes $c_1=-1, c_2=10$ and we prove the existence of a new irreducible component of the moduli space $\mathcal{B}(-1,10)$ of a rank 2 stable bundles with the given Chern classes. We also show that Hartshorne's conditions on a sequence $\mathcal{X}$ of 10 integers are sufficient and necessary for the existence of a stable rank 2 bundle with odd determinant and spectrum $\mathcal{X}$. Furthermore, we prove that the sequence of integers $\{-2^{n-1},-1,0,1^{n-1}\}$ for $ n\geq4$ is realized as the spectrum of a stable rank 2 bundle $\EE$ of odd determinant by computing the minimal generators of its Rao module.

math.AG↗

arXiv2021

Monads and moduli components for stable rank 2 bundles with odd determinant on the projective space

We propose a three-step program for the classification of stable rank 2 bundles on the projective space $\mathbb{P}^3$ inspired by an article by Hartshorne and Rao. While this classification program has been successfully completed for stable rank 2 bundles with even determinant and $c_2\le5$, much less is known for bundles with odd determinant. After revising the known facts about these objects, we list all possible spectra and minimal monads for stable rank 2 bundles with odd determinant and $c_2\le8$. We provide a full classification of all bundles with positive minimal monads, provide a negative answer to a question raised by Hartshorne and Rao, and describe new irreducible components of the moduli spaces of stable rank 2 bundles with odd determinant and $c_2=6,8$.

math.AG↗