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Universidade Federal do Ceará
Universidade Federal do Ceará
On the topological invariance of the algebraic multiplicity of holomorphic foliations
On the topological invariance of the algebraic multiplicity of holomorphic foliations
Resumo: In this talk, I will address one of the most basic and fundamental problems in the theory of foliations and ODEs, the topological invariance of the algebraic multiplicity of a holomorphic foliation. For instance, I will present an adapted version of A'Campo-Lê's Theorem for foliations, i.e., the algebraic multiplicity equal to one is a topological invariant in dimension two. This result is further generalized to higher dimensions under mild conditions; consequently, we prove that saddle-nodes are topological invariant. We prove that the algebraic multiplicity is a topological invariant in several classes of foliations that contain, for instance, the generalized curves and the foliations of the second type.
Resumo: In this talk, I will address one of the most basic and fundamental problems in the theory of foliations and ODEs, the topological invariance of the algebraic multiplicity of a holomorphic foliation. For instance, I will present an adapted version of A'Campo-Lê's Theorem for foliations, i.e., the algebraic multiplicity equal to one is a topological invariant in dimension two. This result is further generalized to higher dimensions under mild conditions; consequently, we prove that saddle-nodes are topological invariant. We prove that the algebraic multiplicity is a topological invariant in several classes of foliations that contain, for instance, the generalized curves and the foliations of the second type.
Finally, I will address a fundamental result by Rosas-Bazan, which states that a homeomorphism extending through a neighbourhood of the exceptional divisor of the first blow-up implies the topological invariance of the algebraic multiplicity. I will show that the result holds if the homeomorphism extends locally near a singularity, even if it does not extend over the entire divisor.
Finally, I will address a fundamental result by Rosas-Bazan, which states that a homeomorphism extending through a neighbourhood of the exceptional divisor of the first blow-up implies the topological invariance of the algebraic multiplicity. I will show that the result holds if the homeomorphism extends locally near a singularity, even if it does not extend over the entire divisor.
This is a joint work with Leonardo M. Câmara and Fernando Reis.
This is a joint work with Leonardo M. Câmara and Fernando Reis.
Data: 17/02/2025
Data: 17/02/2025
Horário: 08h30
Horário: 08h30
Local: Bloco F67 (Dep. de Matemática) da UEM
Local: Bloco F67 (Dep. de Matemática) da UEM
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