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Specialization to the tangent cone and Whitney equisingularity

Arturo Giles Flores (2013)

Bulletin de la Société Mathématique de France

Let ( X , 0 ) be a reduced, equidimensional germ of an analytic singularity with reduced tangent cone ( C X , 0 , 0 ) . We prove that the absence of exceptional cones is a necessary and sufficient condition for the smooth part 𝔛 0 of the specialization to the tangent cone ϕ : 𝔛 to satisfy Whitney’s conditions along the parameter axis Y . This result is a first step in generalizing to higher dimensions Lê and Teissier’s result for hypersurfaces of 3 which establishes the Whitney equisingularity of X and its tangent cone under...

Stabilizers for nondegenerate matrices of boundary format and Steiner bundles.

Carla Dionisi (2004)

Revista Matemática Complutense

In this paper nondegenerate multidimensional matrices of boundary format in V0 ⊗ ... ⊗ Vp are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V0) x ... x SL(Vp)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V0 ⊗ ... ⊗ Vp such that Stab(A)0 ⊆ SL(2) and the equality holds if and only if A belongs to a unique SL(V0) x ... x SL(Vp)-orbit...

Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in 3

M. Burak Erdoğan, Michael Goldberg, Wilhelm Schlag (2008)

Journal of the European Mathematical Society

We present a novel approach for bounding the resolvent of H = - Δ + i ( A · + · A ) + V = : - Δ + L 1 for large energies. It is shown here that there exist a large integer m and a large number λ 0 so that relative to the usual weighted L 2 -norm, ( L ( - Δ + ( λ + i 0 ) ) - 1 ) m < 1 2 2 for all λ > λ 0 . This requires suitable decay and smoothness conditions on A , V . The estimate (2) is trivial when A = 0 , but difficult for large A since the gradient term exactly cancels the natural decay of the free resolvent. To obtain (2), we introduce a conical decomposition of the resolvent and then sum over...

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