Consider a finite groupG acting on a Riemann surface S, and the associated branched Galois cover πG : S → Y = S/G. We introduce the concept of geometric signature for the action of G, and we show that it captures much information: the geometric structure of the lattice of intermediate covers, the isotypical decomposition of the rational representation of the group G acting on the Jacobian varie...

A finite group G acting on an abelian variety A induces a decomposition of A up to isogeny. In this paper we investigate several aspects of this decomposition. We apply the results to the decomposition of the Jacobian variety of a smooth projective curve with G-action. The aim is to express the decomposition in terms of the G-action of the curve. As examples of the results we work out the decom...

The diameter of the inferior vena cava (IVC) measured with echocardiography is clinically used as a parameter to estimate right atrial pressure, which reflects dehydration or overhydration. Because elderly patients fall easily into dehydration, normal values for IVC diameters in elderly patients may be helpful for geriatric medicine. However, normal values of IVC diameter in relation to age hav...

The spatial organization of functional vegetation types in river basins is a major determinant of their runoff production, biodiversity, and ecosystem services. The optimization of different objective functions has been suggested to control the adaptive behavior of plants and ecosystems, often without a compelling justification. Maximum entropy production (MEP), rooted in thermodynamics princip...

We analyze the impact of interior symmetries on the multiplicity of the eigenvalues of the Jacobian matrix at a fully synchronous equilibrium for the coupled cell systems associated to homogeneous networks. We consider also the special cases of regular and uniform networks. It follows from our results that the interior symmetries, as well as the reverse interior symmetries and quotient interior...

In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use this formula to obtain three...

We consider the Sobolev space X = W s,p(Sm;Sk−1). We prove the existence of a robust distributional Jacobian Ju for u ∈ X provided sp ≥ k−1; this generalizes a result of Bourgain, Brezis and the second author [10], where the case m = k is considered. In the critical case where sp = k − 1, we identify the image of the map X 3 u 7→ Ju. This extends a result of Alberti, Baldo and Orlandi [2] for s...

We associate with a plane meromorphic curve f a tree model T (f) based on its contact structure. Then we give a description of the y-derivative of f (resp. the Jacobian J(f, g)) in terms of T (f) (resp. T (fg)). We also characterize the regularity of f in terms of its tree.

Generalizing a result for the binary lens, similar alternative expressions are also given for the Jacobian determinant for a gravitational lens consisting of an arbitrary number of discrete lensing centres, with arbitrary masses and locations in a plane. The results for a binary lens are recovered, agreeing with some already known results, and correcting errors in others.

Article history: Received 9 April 2014 Accepted 3 June 2015 Available online 17 June 2015