Singularities in Geometry, Topology, Foliations and by José Luis Cisneros-Molina, Dũng Tráng Lê, Mutsuo Oka, Jawad

By José Luis Cisneros-Molina, Dũng Tráng Lê, Mutsuo Oka, Jawad Snoussi

This publication positive aspects cutting-edge learn on singularities in geometry, topology, foliations and dynamics and offers an outline of the present nation of singularity idea in those settings.

Singularity idea is on the crossroad of varied branches of arithmetic and technological know-how typically. lately there were notable advancements, either within the conception itself and in its family with different areas.

The contributions during this quantity originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in social gathering of José Seade’s sixtieth Birthday.

It is meant for researchers and graduate scholars drawn to singularity concept and its impression on different fields.

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Singularities in Geometry, Topology, Foliations and Dynamics: A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014

This booklet gains state of the art study on singularities in geometry, topology, foliations and dynamics and gives an outline of the present nation of singularity concept in those settings. Singularity concept is on the crossroad of varied branches of arithmetic and technology usually. lately there were extraordinary advancements, either within the conception itself and in its kinfolk with different parts.

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Additional info for Singularities in Geometry, Topology, Foliations and Dynamics: A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014

Example text

M, where d is a natural number, the φj are convergent Laurent series in ξd−1 (µ−1 (F)) and their support is contained in the cone −Rec(F)∨ . Proof. 2. 4 (Aroca, [2]). Let X be an algebraic variety of CN +M , 0 ∈ X, dim(X) = N. Let U be a neighborhood of 0, and let π be the restriction to X ∩ U of the projection (z1 , . . , zN +M ) → (z1 , . . , zN ). Assume π is a finite morphism. Let δ be a polynomial vanishing on the discriminant locus of π. For each cone σ of N P (δ) associated to a vertex, there exist k ∈ N and M convergent Laurent series s1 , .

This allows to check that the A2 point is on the line x = 0 and the E6 point Q1 (resp. Q2 ) is on the line x = 1 (resp. x = −1). (F2) We factorize the polynomials ha (x0 , y) for x0 = 0, ±1 and we obtain which intersection points are up and down. (F3) For x0 = 0, ±1, let y0 be the y-coordinate of the singular point. For the A2 point, y0 = − a+1 8 we check that the cusp is tangent to the vertical line, and 2 the Puiseux parametrization is of the form y = y0 + y1 x 3 + . . We obtain that y1 < 0 and it implies that the real part of the complex solutions is bigger than the real solution, near x = 0.

Alderete, C. Cabrera, A. Cano and M. Mend [5] C. Frances. Lorentzian Kleinian groups. Comment. Math. , 80(4):883–910, 2005. [6] A. W. Knapp. Lie groups beyond an introduction. Number 140 in Progress in Mathematics. Birkh¨ auser Boston, Boston, MA, second edition edition, 2002. [7] R. S. Kulkarni. Groups with Domains of Discontinuity. Math. , 237(3):253–272, 1978. [8] B. Maskit. Kleinian groups, volume 287 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, New York, 1988.

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