Automorphism groups of non-orientable elliptic-hyperelliptic Klein surfaces with boundary

A classical study about Klein and Riemann surfaces consists in determining their groups of automorphisms. This problem is very difficult in general,and it has been solved for particular families of surfaces or for fixed topological types. In this paper, we calculate the automorphism groups of non-orientable bordered elliptic-hyperelliptic Klein surfaces of algebraic genus p> 5.

Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Deformations of canonical double covers

In this paper we show that if X is a smooth variety of general type of dimension m≥2 for which its canonical map induces a double cover onto Y, where Y is the projective space, a smooth quadric hypersurface or a smooth projective bundle over P1, embedded by a complete linear series, then the general deformation of the canonical morphism of X is again canonical and induces a double cover. The second part of the article proves the non-existence of canonical double structures on the rational varieties above mentioned. Our results have consequences for the moduli of varieties of general type of arbitrary dimension, since they show that infinitely many moduli spaces of higher dimensional varieties of general type have an entire “hyperelliptic��� component. This is in sharp contrast with the case of curves or surfaces of lower Kodaira dimension.