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Universidade de Integração Internacional da Lusofonia Afro-Brasileira
Universidade de Integração Internacional da Lusofonia Afro-Brasileira
Deforming the weighted-homogeneous foliation, and trivializing families of semi-weighted homogeneous ICIS.
Deforming the weighted-homogeneous foliation, and trivializing families of semi-weighted homogeneous ICIS.
Resumo: Let X_o := V(f_p) ⊂ (K^N,o) be a weighted-homogeneous complete intersection germ (with arbitrary singularities, possibly non-reduced). Let {γ_s}_s∈S be the corresponding foliation of K^N by weighted- homogeneous real arcs. Take a deformation by higher order terms, Xϵ := V(f_p + ϵ · f _{>p}). Does the foliation {γ_s} deform compatibly with X?
We identify the “obstruction locus”, Σ ⊂ X_o, outside of which such a deformation does exist, and possesses exceptionally nice properties. Using this deformed foliation we construct contact trivialization of the family f _p + ϵ · f _{>p} by homeomorphisms that are real analytic (resp. Nash) of the origin, differentiable at the origin, whose presentation in weighted-polar coordinates is globally real-analytic (resp. globally Nash), and with controlled Lipschitz/C^1-properties.
This is a joint work with Dmitry Kerner (Ben Gurion University of the Negev).
Keywords: Singularity Theory, foliations by arcs, blow-analytic trivializations, finite determinacy, weighted-homogeneous map-germs.
Data: 19/02/2025
Data: 19/02/2025
Horário: 14h00
Horário: 14h00
Local: Bloco F67 (Dep. de Matemática) da UEM
Local: Bloco F67 (Dep. de Matemática) da UEM
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