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Topology of arrangements and position of singularities

Enrique Artal Bartolo (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees)...

Topology of real algebraic T-surfaces.

Ilia Itenberg (1997)

Revista Matemática de la Universidad Complutense de Madrid

The paper is devoted to algebraic surfaces which can be obtained using a simple combinatorial procedure called the T-construction. The class of T-surfaces is sufficiently rich: for example, we construct T-surfaces of an arbitrary degree in RP³ which are M-surfaces. We also present a construction of T-surfaces in RP³ with dim H1 (RX; Z/2) > h1, 1(CX), where RX and CX are the real and the complex point sets of the surface.

Top-stable and layer-stable degenerations and hom-order

S. O. Smalø, A. Valenta (2007)

Colloquium Mathematicae

Using geometrical methods, Huisgen-Zimmermann showed that if M is a module with simple top, then M has no proper degeneration M < d e g N such that t M / t + 1 M ≃ t N / t + 1 N for all t. Given a module M with square-free top and a projective cover P, she showed that d i m k H o m ( M , M ) = d i m k H o m ( P , M ) if and only if M has no proper degeneration M < d e g N where M/M ≃ N/N. We prove here these results in a more general form, for hom-order instead of degeneration-order, and we prove them algebraically. The results of Huisgen-Zimmermann follow as consequences from our results....

Tore de l’inertie modérée

Lionel Dorat (2008)

Journal de Théorie des Nombres de Bordeaux

Nous étudions dans cet article les représentations cristallines vérifiant les conditions de Fontaine-Laffaille, en particulier l’image de l’inertie modérée. A partir de cette image, nous définissons un tore et une représentation de ce tore, dont nous montrons qu’elle est à valeurs (sous certaines conditions) dans l’adhérence de Zariski de l’image de la représentation galoisienne, et nous donnons le lien entre cette représentation du tore et le groupe à un paramètre de Hodge-Tate (tout ceci à l’aide...

Torelli theorem for stable curves

Lucia Caporaso, Filippo Viviani (2011)

Journal of the European Mathematical Society

We study the Torelli morphism from the moduli space of stable curves to the moduli space of principally polarized stable semi-abelic pairs. We give two characterizations of its fibers, describe its injectivity locus, and give a sharp upper bound on the cardinality of finite fibers. We also bound the dimension of infinite fibers.

Toric and tropical compactifications of hyperplane complements

Graham Denham (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

These lecture notes survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we review the Gel ' fand-MacPherson construction, Kapranov’s visible contours compactification, and De Concini and Procesi’s wonderful compactification. We explain how these constructions are unified by some ideas from the modern origins of tropical geometry.

Toric embedded resolutions of quasi-ordinary hypersurface singularities

Pedro D. González Pérez (2003)

Annales de l’institut Fourier

We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485- 503. In the first procedure the singularity is...

Torsion and Tamagawa numbers

Dino Lorenzini (2011)

Annales de l’institut Fourier

Let K be a number field, and let A / K be an abelian variety. Let c denote the product of the Tamagawa numbers of A / K , and let A ( K ) tors denote the finite torsion subgroup of A ( K ) . The quotient c / | A ( K ) tors | is a factor appearing in the leading term of the L -function of A / K in the conjecture of Birch and Swinnerton-Dyer. We investigate in this article possible cancellations in this ratio. Precise results are obtained for elliptic curves over ℚ or quadratic extensions K / ℚ , and for abelian surfaces A / ℚ . The smallest possible ratio...

Torsion des courbes elliptiques sur les corps cubiques

Pierre Parent (2000)

Annales de l'institut Fourier

On donne la liste (à un élément près) des nombres premiers qui sont l’ordre d’un point de torsion d’une courbe elliptique sur un corps de nombres de degré trois.

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