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Displaying 61 –
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177
On généralise dans cet article la notion de filtration de Harder-Narasimhan au cas des
fibrés complexes sur une variété presque complexe compacte d'une part, et au cas des
faisceaux cohérents sans torsion sur une variété holomorphe d'autre part. On démontre,
dans les deux cas, l'existence d'un déstabilisant maximal. On obtient un théorème de
convergence en famille et par là-même l'ouverture de la stabilité en déformation.
For germs of singularities of holomorphic foliations in which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.
We study some algebraic properties of commutators of Toeplitz operators on the Hardy space of the bidisk. First, for two symbols where one is arbitrary and the other is (co-)analytic with respect to one fixed variable, we show that there is no nontrivial finite rank commutator. Also, for two symbols with separated variables, we prove that there is no nontrivial finite rank commutator or compact commutator in certain cases.
The Gleason problem is solved on real analytic pseudoconvex domains in . In this case the weakly pseudoconvex points can be a two-dimensional subset of the boundary. To reduce the Gleason problem to a question it is shown that the set of Kohn-Nirenberg points is at most one-dimensional. In fact, except for a one-dimensional subset, the weakly pseudoconvex boundary points are -points as studied by Range and therefore allow local sup-norm estimates for .
This paper deals with the finiteness problem of meromorphic funtions on an annulus sharing four values regardless of multiplicity. We prove that if three admissible meromorphic functions , , on an annulus share four distinct values regardless of multiplicity and have the complete identity set of positive counting function, then or or . This result deduces that there are at most two admissible meromorphic functions on an annulus sharing a value with multiplicity truncated to level and...
We prove some finiteness theorems for differential nondegenerate meromorphic mappings of into ℙⁿ(ℂ) which share n+3 hyperplanes.
We study here several finiteness problems concerning affine Nash manifolds and Nash subsets . Three main results are: (i) A Nash function on a semialgebraic subset of has a Nash extension to an open semialgebraic neighborhood of in , (ii) A Nash set that has only normal crossings in can be covered by finitely many open semialgebraic sets equipped with Nash diffeomorphisms such that , (iii) Every affine Nash manifold with corners is a closed subset of an affine Nash manifold...
We study the integrals of real functions which are finite compositions of globally
subanalytic maps and real power functions. These functions have finiteness properties
very similar to those of subanalytic functions. Our aim is to investigate how such
finiteness properties can remain when taking the integrals of such functions. The main
result is that for almost all power maps arising in a -function, its
integration leads to a non-oscillating function. This can be seen as a generalization of
Varchenko...
We show that for each genus there are only finitely many algebraically primitive Teichmüller curves , such that (i) lies in the hyperelliptic locus and (ii) is generated by an abelian differential with two zeros of order . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.
We consider a contractible closure of the space of Legendrian knots in the standard contact 3-space. We show that in this context the space of finite-type complex-valued invariants of Legendrian knots is isomorphic to that of framed knots in with an extra order 1 generator (Maslov index) added.
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