3,751 research outputs found
Equivalent birational embeddings II: divisors
Two divisors in are said to be Cremona equivalent if there is a
Cremona modification sending one to the other. We produce infinitely many non
equivalent divisorial embeddings of any variety of dimension at most 14. Then
we study the special case of plane curves and rational hypersurfaces. For the
latter we characterise surfaces Cremona equivalent to a plane.Comment: v2 Exposition improved, thanks to referee, unconditional
characterization of surfaces Cremona equivalent to a plan
Birational geometry of rational quartic surfaces
Two birational subvarieties of P^n are called Cremona equivalent if there is
a Cremona modification of P^n mapping one to the other. If the codimension of
the varieties is at least 2 then they are always Cremona Equivalent. For
divisors the question is much more subtle and a general answer is unknown. In
this paper I study the case of rational quartic surfaces and prove that they
are all Cremona equivalent to a plane.Comment: Improved exposition after referee comments, 10 page
Birational geometry of Fano direct products
We prove birational superrigidity of direct products of primitive Fano varieties of the following two types: either
is a general hypersurface of degree , ,
or is a general double space of index
1, . In particular, each structure of a rationally connected fiber
space on is given by a projection onto a direct factor. The proof is based
on the connectedness principle of Shokurov and Koll\' ar and the technique of
hypertangent divisors.Comment: 38 pages, LaTeX. This is the final enlarged version of the pape
Fano resonances and decoherence in transport through quantum dots
A tunable microwave scattering device is presented which allows the
controlled variation of Fano line shape parameters in transmission through
quantum billiards. We observe a non-monotonic evolution of resonance parameters
that is explained in terms of interacting resonances. The dissipation of
radiation in the cavity walls leads to decoherence and thus to a modification
of the Fano profile. We show that the imaginary part of the complex Fano
q-parameter allows to determine the absorption constant of the cavity. Our
theoretical results demonstrate further that the two decohering mechanisms,
dephasing and dissipation, are equivalent in terms of their effect on the
evolution of Fano resonance lineshapes.Comment: 9 pages, 7 figures, submitted to Physica E (conference proceedings
Tunable Fano Resonances in Transport through Microwave Billiards
We present a tunable microwave scattering device that allows the controlled
variation of Fano line shape parameters in transmission through quantum
billiards. Transport in this device is nearly fully coherent. By comparison
with quantum calculations, employing the modular recursive Green's-function
method, the scattering wave function and the degree of residual decoherence can
be determined. The parametric variation of Fano line shapes in terms of
interacting resonances is analyzed.Comment: 5 pages, 4 figures, submitted to Phys. Rev.
Emerging beam resonances in atom diffraction from a reflection grating
We report on the observation of emerging beam resonances, well known as
Rayleigh-Wood anomalies and threshold resonances in photon and electron
diffraction, respectively, in an atom-optical diffraction experiment.
Diffraction of He atom beams reflected from a blazed ruled grating at grazing
incidence has been investigated. The total reflectivity of the grating as well
as the intensities of the diffracted beams reveal anomalies at the Rayleigh
angles of incidence, i.e., when another diffracted beam merges parallel to the
grating surface. The observed anomalies are discussed in terms of the classical
wave-optical model of Rayleigh and Fano.Comment: 4 pages, 3 figure
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