The weight-monodromy conjecture claims the coincidence of the shifted weight filtration and the monodromy filtration on étale cohomology of a proper smooth variety over a complete discrete valuation field. Although it was already proved in some cases, the case of dimension ≥ 3 in mixed characteristic is still unproved up to now. The aim of this paper is to prove the weight-monodromy conjecture ...

The change in the energy level structure of a bent molecule as it starts to sample linear geometries has been discussed in terms of monodromy found in simple two-dimensional model problems. Infrared spectra of hot (T 3000 K) water are analysed for transitions involving states with high bending excitation which can sample linear HOH geometries. One hundred and thirty four new experimental energy...

The Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing pcurvatures for almost all p, has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on P1−{0, 1,∞}. We prove a variant of this conjecture for P1−{0, 1,∞}, which asserts that if the equation satisfies a certain conve...

1.1. Let f and f ′ be germs of analytic functions on smooth complex analytic varieties X and X ′ and consider the function f ⊕ f ′ on X × X ′ given by f ⊕ f (x, x) = f(x) + f (x). The Thom-Sebastiani Theorem classically states that the monodromy of f ⊕ f ′ on the nearby cycles is isomorphic to the product of the monodromy of f and the monodromy of f ′ (in the original form of the Theorem [18] t...

Trivial choreographies are special periodic solutions of the planar three-body problem. In this work we use a modified Newton’s method based on continuous analog and high precision arithmetic for specialized numerical search new trivial choreographies. As result computed database 462 such orbits, including 397 ones. The initial conditions periods all found given with 180 correct decimal digits....

Let R be a complete discrete valuation ring of mixed characteristic (0, p) with fraction field K. We study stable models of p-cyclic covers of PK . First, we determine the monodromy extension, the monodromy group, its filtration and the Swan conductor for special covers of arbitrarily high genus with potential good reduction. In the case p = 2 we consider hyperelliptic curves of genus 2.

We study the vanishing neighbourhood of non-isolated singularities of functions on singular spaces by associating a general linear function. We use the carrousel monodromy in order to show how to get a better control over the attaching of thimbles. For one dimensional singularities, we prove obstructions to integer (co)homology groups and to the eigenspaces of the monodromy via monodromies of n...

We discuss N = 2 SU(2) Yang-Mills gauge theories coupled with Nf (= 2, 3) massive hypermultiplets in the weak coupling limit. We determine the exact massive prepotentials and the monodromy matrices around the weak coupling limit. We also study that the double scaling limit of these massive theories and find that the massive Nf − 1 theory can be obtained from the massive Nf theory. New formulae ...

Let G be a finite group. By Riemann’s Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus many problems on algebraic curves require the computation of braid orbits. In this paper we describe an implementation of this computation. We discuss several applications, including the cl...

A local system, defined on the complement of a divisor Z ⊆ X in a complex manifold, can in general not be extended to all of X because of local monodromy. This paper describes the construction of a normal analytic space that naturally extends the étale space T of the local system, in the case when Z is a divisor with normal crossings and the local system has unipotent local monodromy.