arXiv subjects

Jose Ignacio Cogolludo-Agustín

Publications and source records attributed to Jose Ignacio Cogolludo-Agustín.

2 recordsLinked to original sources

arXiv2026

On modular inequalities for plane projective curves

We introduce modular inequalities for complements of plane curves, based on a Combinatorial Aomoto complex construction associated with the weak combinatorial type of a curve. We use this as a tool to investigate twisted Alexander polynomials, in particular to study the characteristic polynomial of the Milnor fiber associated to a projective plane curve, i.e. the classical Alexander polynomial. We give criteria for the non-triviality of the resonance in degree $1$, over a positive characteristic field, for curves with quasi fiber--type structure and we compute lower bounds for the multiplicities of some roots of twisted Alexander polynomials for this type of curves. We apply these results to theoretically compute the multiplicities of certain roots of twisted Alexander polynomials for fiber--type curves.

math.AT↗

arXiv2023

On the Sigma invariants of even Artin groups of FC-type

In this paper we study Sigma invariants of even Artin groups of FC-type, extending some known results for right-angled Artin groups. In particular, we define a condition that we call the strong homological $n$-link condition for a graph $Γ$ and prove that it gives a sufficient condition for a character $χ:A_Γ\to \mathbb{Z}$ to satisfy $[χ]\inΣ^n(A_Γ,\mathbb{Z})$. This implies that the kernel $A^χ_Γ=\ker χ$ is of type $FP_n$. The homotopy counterpart is also proved. Partial results on the converse are discussed. We also provide a general formula for the free part of $H_n(A^χ_Γ;\mathbb{F})$ as an $\mathbb{F}[t^{\pm 1}]$-module with the natural action induced by $χ$. This gives a characterization of when $H_n(A^χ_Γ;\mathbb{F})$ is a finite dimensional vector space over $\mathbb{F}$. In the last version we correct a problem in the proof of Lemma 4.3 and also a remark at the end of subsection 3.3.

math.GR↗