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math.AC2024
Rose-Terao-Yuzvinsky theorem for reduced forms
Ricardo Burity, Zaqueu Ramos, Aron Simis +1
Yuzvinsky and Rose-Terao have shown that the homological dimension of the gradient ideal of the defining polynomial of a generic hyperplane arrangement is maximum possible. In this…
math.AC2024
Matrices over polynomial rings approached by commutative algebra
Zaqueu Ramos, Aron Simis
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related…
math.AC2024
Bounds on the degrees of vector fields
Marc Chardin, S. Hamid Hassanzadeh, Claudia Polini +2
In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of t…