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Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups

Ngaiming Mok (2000)

Annales de l'institut Fourier

We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then H 1 ( G a m m a , Φ ) ≠ 0 for some unitary representation Φ . By our earlier work there exists a d -closed holomorphic 1-form with coefficients twisted by some unitary representation Φ ' , possibly non-isomorphic to Φ . Taking norms we obtains a positive...

Fibre de Milnor motivique à l’infini et composition avec un polynôme non dégénéré

Michel Raibaut (2012)

Annales de l’institut Fourier

Soit k un corps de caractéristique nulle, P un polynôme de Laurent en d variables, à coefficients dans k et non dégénéré pour son polyèdre de Newton à l’infini. Soit d fonctions non constantes f l à variables séparées et définies sur des variétés lisses. A la manière de Guibert, Loeser et Merle, dans le cas local, nous calculons dans cet article, la fibre de Milnor motivique à l’infini de la composée P ( f ) en termes du polyèdre de Newton à l’infini de P . Pour P égal à la somme x 1 + x 2 nous obtenons une formule...

Fibrés vectoriels de rang deux sur ℙ 2 provenant d’un revêtement double

Jean Vallès (2009)

Annales de l’institut Fourier

Depuis Schwarzenberger et son célèbre article intitulé «  Vector bundles on the projective plane  », on sait que tout fibré de rang deux sur ℙ 2 ( ℂ ) peut être défini comme l’image directe d’un faisceau inversible sur une surface recouvrant doublement le plan. Ce théorème suggère d’étudier les fibrés de rang deux en fonction de la courbe de ramification du revêtement dont ils proviennent.Ainsi, dans la première partie on démontre que, étant donné un revêtement ramifié le long d’une courbe irréductible...

Finiteness results for Teichmüller curves

Martin Möller (2008)

Annales de l’institut Fourier

We show that for each genus there are only finitely many algebraically primitive Teichmüller curves C , such that (i) C lies in the hyperelliptic locus and (ii) C is generated by an abelian differential with two zeros of order g - 1 . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.

Fragmented deformations of primitive multiple curves

Jean-Marc Drézet (2013)

Open Mathematics

A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization...

Galois actions on Néron models of Jacobians

Lars H. Halle (2010)

Annales de l’institut Fourier

Let X be a smooth curve defined over the fraction field K of a complete discrete valuation ring R . We study a natural filtration of the special fiber of the Néron model of the Jacobian of X by closed, unipotent subgroup schemes. We show that the jumps in this filtration only depend on the fiber type of the special fiber of the minimal regular model with strict normal crossings for X over R , and in particular are independent of the residue characteristic. Furthermore, we obtain information about...

Galois Covers and the Hilbert-Grunwald Property

Pierre Dèbes, Nour Ghazi (2012)

Annales de l’institut Fourier

Our main result combines three topics: it contains a Grunwald-Wang type conclusion, a version of Hilbert’s irreducibility theorem and a p -adic form à la Harbater, but with good reduction, of the Regular Inverse Galois Problem. As a consequence we obtain a statement that questions the RIGP over ℚ . The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.

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