2,954 research outputs found
Low Rank Vector Bundles on the Grassmannian G(1,4)
Here we define the concept of -regularity for coherent sheaves on the
Grassmannian G(1,4) as a generalization of Castelnuovo-Mumford regularity on
. In this setting we prove analogs of some classical properties. We
use our notion of -regularity in order to prove a splitting criterion for
rank 2 vector bundles with only a finite number of vanishing conditions. In the
second part we give the classification of rank 2 and rank 3 vector bundles
without "inner" cohomology (i.e. H^i_*(E)=H^i(E\otimes\Q)=0 for any
) on G(1,4) by studying the associated monads.Comment: 11 pages, no figure
The distance function from a real algebraic variety
For any (real) algebraic variety in a Euclidean space endowed with a
nondegenerate quadratic form , we introduce a polynomial
which, for any , has among its roots the
distance from to . The degree of is the {\em
Euclidean Distance degree} of . We prove a duality property when is a
projective variety, namely
where
is the dual variety of . When is transversal to the isotropic
quadric , we prove that the ED polynomial of is monic and the zero locus
of its lower term is .Comment: 24 pages, 4 figures, accepted for publication in Computer Aided
Geometric Desig
The curve of lines on a prime Fano threefold of genus 8
We show that a general prime Fano threefold X of genus 8 can be reconstructed
from the pair , where is its Fano curve of lines and
is the theta-characteristic which gives a natural embedding
\Gamma \subset \matbb{P}^5.Comment: 24 pages, misprints corrected, to appear in International Journal of
Mathematic
Fel Oscillators with Tapered Undulators: Inclusion of Harmonic Generation and Pulse Propagation
We review the theory of FEL oscillators operating with tapered undulators. We
consider the case of a uniform tapering and introduce a parameter which
characterizes the effect of the tapering on the gain and on the saturation
intensity. We analyze the effect of the tapering on the FEL dynamics by
including the pulse propagation effects too. We analyze the importance of
tapering as a tool to model the optical pulse shapes and to control the higher
harmonic intensities
Hybrid Superconducting Neutron Detectors
A new neutron detection concept is presented that is based on superconductive
niobium (Nb) strips coated by a boron (B) layer. The working principle of the
detector relies on the nuclear reaction 10B+n + 7Li ,
with and Li ions generating a hot spot on the current-biased Nb strip
which in turn induces a superconducting-normal state transition. The latter is
recognized as a voltage signal which is the evidence of the incident neutron.
The above described detection principle has been experimentally assessed and
verified by irradiating the samples with a pulsed neutron beam at the ISIS
spallation neutron source (UK). It is found that the boron coated
superconducting strips, kept at a temperature T = 8 K and current-biased below
the critical current Ic, are driven into the normal state upon thermal neutron
irradiation. As a result of the transition, voltage pulses in excess of 40 mV
are measured while the bias current can be properly modulated to bring the
strip back to the superconducting state, thus resetting the detector.
Measurements on the counting rate of the device are presented and the future
perspectives leading to neutron detectors with unprecedented spatial
resolutions and efficiency are highlighted.Comment: 8 pages 6 figure
Asymptotics of degrees and ED degrees of Segre products
Two fundamental invariants attached to a projective variety are its classical algebraic degree and its Euclidean Distance degree (ED degree). In this paper, we study the asymptotic behavior of these two degrees of some Segre products and their dual varieties. We analyze the asymptotics of degrees of (hypercubical) hyperdeterminants, the dual hypersurfaces to Segre varieties. We offer an alternative viewpoint on the stabilization of the ED degree of some Segre varieties. Although this phenomenon was incidentally known from Friedland-Ottaviani's formula expressing the number of singular vector tuples of a general tensor, our approach provides a geometric explanation. Finally, we establish the stabilization of the degree of the dual variety of a Segre product X×Qn, where X is a projective variety and Qn⊂Pn+1 is a smooth quadric hypersurface
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