Search results for " monodromy"
showing 9 items of 9 documents
Hurwitz spaces of coverings with two special fibers and monodromy group a Weyl group of typeBd
2012
f! Y; where is a degree-two coverings with n1 branch points and branch locus D and f is a degree-d coverings with n2 points of simple branching and two special points whose local monodromy is given by e and q, respectively. Furthermore the covering f has monodromy group Sd and f. D /\ D fD? where D f denotes the branch locus of f . We prove that the corresponding Hurwitz spaces are irreducible under the hypothesis n2 s r dC 1.
A note on coverings with special fibres and monodromy group $ S_{d}$
2012
We consider branched coverings of degree over with monodromy group , points of simple branching, special points and fixed branching data at the special points, where is a smooth connected complex projective curve of genus , and , are integers with . We prove that the corresponding Hurwitz spaces are irreducible if .
On the irreducibility of Hurwitz spaces of coverings with an arbitrary number of special points
2013
In this paper we study Hurwitz spaces of coverings of Y with an arbitrary number of special points and with monodromy group a Weyl group of type D_d, where Y is a smooth, complex projective curve. We give conditions for which these spaces are irreducible.
About the role of hamiltonian singularities in controlled systems : applications in quantum mechanics and nonlinear optics
2012
This thesis has two goals: the first one is to improve the control techniques in quantum mechanics, and more specifically in NMR, by using the tools of geometric optimal control. The second one is the study of the influence of Hamiltonian singularities in controlled systems. The chapter about optimal control study three classical problems of NMR : the inversion problem, the influence of the radiation damping term, and the steady state technique. Then, we apply the geometric optimal control to the problem of the population transfert in a three levels quantum system to recover the STIRAP scheme.The two next chapters study Hamiltonian singularities. We show that they allow to control the polar…
On the irreducibility of Hurwitz spaces of coverings with two special fibers
2012
MR 3004007 Reviewed Chretien P. and Matignon M. Maximal wild monodromy in unequal characteristic. Journal of Number Theory (2013) 133, 1389--1408. Re…
2013
Let R be a complete discrete valuation ring of mixed characteristic (0, p) with fraction field K. The stable reduction theorem affirms that given a smooth, projective, geometrically connected curve over K, C/K, with genus \geq 2, there exists a unique finite Galois extension M/K minimal for the inclusion relation such that C_{M}:= C x M has stable reduction over M. A such extension is called monodromy extension of C/K and the Galois group Gal(M/K) is called the monodromy group of C/K. In this paper, the authors study stable models of p-cyclic covers of P^1_K. At first, they work with covers of arbitrarily high genus having potential good reduction. In particular, they determine for such cov…
Integrable Hamiltonian systems with swallowtails
2010
International audience; We consider two-degree-of-freedom integrable Hamiltonian systems with bifurcation diagrams containing swallowtail structures. The global properties of the action coordinates in such systems together with the parallel transport of the period lattice and corresponding quantum cells in the joint spectrum are described in detail. The relation to the concept of bidromy which was introduced in Sadovski´ı and Zhilinski´ı (2007 Ann. Phys. 322 164–200) is discussed.
Irreducible components of Hurwitz spaces of coverings with two special fibers
2013
In this paper we prove new results of irreducibility for Hurwitz spaces of coverings whose monodromy group is a Weyl group of type B_d and whose local monodromies are all reflections except two.
Sur le rôle des singularités hamiltoniennes dans les systèmes contrôlés : applications en mécanique quantique et en optique non-linéaire.
2012
This thesis has two goals: the first one is to improve the control techniques in quantum mechanics, and more specifically in NMR, by using the tools of geometric optimal control. The second one is the study of the influence of Hamiltonian singularities in controlled systems. The chapter about optimal control study three classical problems of NMR : the inversion problem, the influence of the radiation damping term, and the steady state technique. Then, we apply the geometric optimal control to the problem of the population transfert in a three levels quantum system to recover the STIRAP scheme.The two next chapters study Hamiltonian singularities. We show that they allow to control the polar…