760 research outputs found
More cubic surfaces violating the Hasse principle
We generalize L.J. Mordell's construction of cubic surfaces for which the
Hasse principle fails
The Hasse principle for lines on diagonal surfaces
Given a number field and a positive integer , in this paper we
consider the following question: does there exist a smooth diagonal surface of
degree in over which contains a line over every
completion of , yet no line over ? We answer the problem using Galois
cohomology, and count the number of counter-examples using a result of
Erd\H{o}s.Comment: 14 page
On the Brauer-Manin obstruction for degree four del Pezzo surfaces
We show that, for every integer and every finite set of
places, there exists a degree del Pezzo surface over such
that and the
Brauer-Manin obstruction works exactly at the places in . For , we
prove that in all cases, with the exception of , this surface
may be chosen diagonalizably over
Large deviations for the capacity in dynamic spatial relay networks
We derive a large deviation principle for the space-time evolution of users
in a relay network that are unable to connect due to capacity constraints. The
users are distributed according to a Poisson point process with increasing
intensity in a bounded domain, whereas the relays are positioned
deterministically with given limiting density. The preceding work on capacity
for relay networks by the authors describes the highly simplified setting where
users can only enter but not leave the system. In the present manuscript we
study the more realistic situation where users leave the system after a random
transmission time. For this we extend the point process techniques developed in
the preceding work thereby showing that they are not limited to settings with
strong monotonicity properties.Comment: 24 pages, 1 figur
Sharp thresholds for Gibbs-non-Gibbs transition in the fuzzy Potts model with a Kac-type interaction
We investigate the Gibbs properties of the fuzzy Potts model on the
d-dimensional torus with Kac interaction. We use a variational approach for
profiles inspired by that of Fernandez, den Hollander and Mart{\i}nez for their
study of the Gibbs-non-Gibbs transitions of a dynamical Kac-Ising model on the
torus. As our main result, we show that the mean-field thresholds dividing
Gibbsian from non-Gibbsian behavior are sharp in the fuzzy Kac-Potts model with
class size unequal two. On the way to this result we prove a large deviation
principle for color profiles with diluted total mass densities and use
monotocity arguments.Comment: 20 page
On the frequency of algebraic Brauer classes on certain log K3 surfaces
Given systems of two (inhomogeneous) quadratic equations in four variables,
it is known that the Hasse principle for integral points may fail. Sometimes
this failure can be explained by some integral Brauer-Manin obstruction. We
study the existence of a non-trivial algebraic part of the Brauer group for a
family of such systems and show that the failure of the integral Hasse
principle due to an algebraic Brauer-Manin obstruction is rare, as for a
generic choice of a system the algebraic part of the Brauer-group is trivial.
We use resolvent constructions to give quantitative upper bounds on the number
of exceptions.Comment: 13 page
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