We complement Catanese’ s results on isotrivially fibred surfaces by completely describing the components containing an isotrivial surface with monodromy group Z/2Z. We also give an example for deformation equivalent isotrivial surfaces with different monodromy group. Mathematics Subject Classification 2000. 14J10, 14D06

Introduction Lecture 1. Algebraic properties of correlators in 2D topological field theory. Moduli of a 2D TFT and WDVV equations of associativity. Lecture 2. Equations of associativity and Frobenius manifolds. Deformed flat connection and its monodromy at the origin. Lecture 3. Semisimplicity and canonical coordinates. Lecture 4. Classification of semisimple Frobenius manifolds. Lecture 5. Mon...

We propose to build in this paper a combinatorial invariant, called the ”spectral monodromy” from the spectrum of a single (non-selfadjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting selfadjoint h-pseudodifferential operators, given ...

This is the third in a series of three papers on quantum billiards with elliptic and ellipsoidal boundaries. In the present paper we show that the integrable billiard inside a prolate ellipsoid has an isolated singular point in its bifurcation diagram and, therefore, exhibits classical and quantum monodromy. We derive the monodromy matrix from the requirement of smoothness for the action variab...

In earlier work [Ka-RLSFM], Katz exhibited some very simple one parameter families of exponential sums which gave rigid local systems on the affine line in characteristic p whose geometric (and usually, arithmetic) monodromy groups were SL2(q), and he exhibited other such very simple families giving SU3(q). [Here q is a power of the characteristic p, and p is odd.] In this paper, we exhibit equ...

To decompose solution sets of polynomial systems into irreducible components, homotopy continuation methods generate the action of a natural monodromy group which partially classi es generic points onto their respective irreducible components. As illustrated by the performance on several test examples, this new method achieves a great increase in speed and accuracy, as well as improved numerica...

We consider the following question: given A ∈ SL(2,R), which potentials q for the second order Sturm-Liouville problem have A as its Floquet multiplier? More precisely, define the monodromy map μ taking a potential q ∈ L2([0, 2π]) to μ(q) = Φ̃(2π), the lift to the universal cover G = ̃ SL(2,R) of SL(2,R) of the fundamental matrix map Φ : [0, 2π] → SL(2,R), Φ(0) = I, Φ(t) = (

The Schlesinger equations S(n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m×m matrix algebras equipped with the standard linear Poisson bracket. In this paper we address the problem of reduction of particular solutions of “more com...

Using the potential surface of Essers, Tennyson, and Wormer in [Chem. Phys. Lett. 89 (1982) 223], we show that the system of bending vibrational states of the isomerizing molecule LiNC/NCLi has monodromy. On the basis of a deformed spherical pendulum model, we explain dynamical and geometric reasons of this phenomenon and of its absence in the similar system HCN/CNH. 2003 Elsevier B.V. All righ...

The notion of local equivalence relation on a topological space is generalized to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation of a monodromy principle on the extendability of local Lie morphisms.  2001 Elsevier Science B.V. All rights reserved. AMS classification: 58H05; 22A22; 18F20