1,305 research outputs found
A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space
A generalized Bogomolov-Gieseker inequality for tilt-stable complexes on a
smooth projective threefold was conjectured by Bayer, Toda, and the author. We
show that such inequality holds true in general, if it holds true when the
polarization is sufficiently small. As an application, we prove it for the
three-dimensional projective space.Comment: 17 pages, 4 figure
Stability conditions under change of base field
We investigate the behaviour of Bridgeland stability conditions under change
of base field with particular focus on the case of finite Galois extensions. In
particular, we prove that for a variety X over a field K and a finite Galois
extension L/K the stability manifold of X embeds as a closed submanifold into
the stability manifold of the base change variety.Comment: 18 pages; v2: minor revisio
Lattices, cohomology and models of six dimensional almost abelian solvmanifolds
We construct lattices on six dimensional not completely solvable almost
abelian Lie groups, for which the Mostow condition does not hold. For the
corresponding compact quotients, we compute the de Rham cohomology (which does
not agree in general with the Lie algebra one) and a minimal model. We show
that some of these solvmanifolds admit not invariant symplectic structures and
we study formality and Lefschetz properties.Comment: arXiv admin note: text overlap with arXiv:1003.3774 by other author
Classification of Poisson surfaces
We study complex projective surfaces admitting a Poisson structure. We prove
a classification theorem and count how many independent Poisson structures
there are on a given Poisson surface.Comment: LaTeX file, 8 pages; to be published in "Communications in
Contemporary Mathematics
Collective modes across the soliton-droplet crossover in binary Bose mixtures
We study the collective modes of a binary Bose mixture across the soliton to
droplet crossover in a quasi one dimensional waveguide with a beyond-mean-field
equation of state and a variational Gaussian ansatz for the scalar bosonic
field of the corresponding effective action. We observe a sharp difference in
the collective modes in the two regimes. Within the soliton regime modes vary
smoothly upon the variation of particle number or interaction strength. On the
droplet side collective modes are inhibited by the emission of particles. This
mechanism turns out to be dominant for a wide range of particle numbers and
interactions. In a small window of particle number range and for intermediate
interactions we find that monopole frequency is likely to be observed. In the
last part we focus on the spin-dipole modes for the case of equal intraspecies
interactions and equal equilibrium particle numbers in the presence of a weak
longitudinal confinement. We found that such modes might be unobservable in the
real-time dynamics close to the equilibrium as their frequency is higher than
the particle emission spectrum by at least one order of magnitude in the
droplet phase. Our results are relevant for experiments with two-component BECs
for which we provide realistic parameters.Comment: Accepted for Publication in PR
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