5,612 research outputs found
Coble fourfold, -invariant quartic threefolds, and Wiman-Edge sextics
We construct two small resolutions of singularities of the Coble fourfold
(the double cover of the four-dimensional projective space branched over the
Igusa quartic). We use them to show that all -invariant three-dimensional
quartics are birational to conic bundles over the quintic del Pezzo surface
with the discriminant curves from the Wiman-Edge pencil. As an application, we
check that -invariant three-dimensional quartics are unirational, obtain
new proofs of rationality of four special quartics among them and irrationality
of the others, and describe their Weil divisor class groups as
-representations.Comment: 57 pages; v2: minor changes; v3: referee's comments taken into
account; v4: published versio
Equations, inequations and inequalities characterizing the configurations of two real projective conics
Couples of proper, non-empty real projective conics can be classified modulo
rigid isotopy and ambient isotopy.
We characterize the classes by equations, inequations and inequalities in the
coefficients of the quadratic forms defining the conics.
The results are well--adapted to the study of the relative position of two
conics defined by equations depending on parameters.Comment: 31 pages. See also
http://emmanuel.jean.briand.free.fr/publications/twoconics/ Added references
to important prior work on the subject. The title changed accordingly. Some
typos and imprecisions corrected. To be published in Applicable Algebra in
Engineering, Communication and Computin
Two-dimensional quasineutral description of particles and fields above discrete auroral arcs
Stationary hot and cool particle distributions in the auroral magnetosphere are modelled using adiabatic assumptions of particle motion in the presence of broad-scale electrostatic potential structure. The study has identified geometrical restrictions on the type of broadscale potential structure which can be supported by a multispecies plasma having specified sources and energies. Without energization of cool thermal ionospheric electrons, a substantial parallel potential drop cannot be supported down to altitudes of 2000 km or less. Observed upward-directed field-aligned currents must be closed by return currents along field lines which support little net potential drop. In such regions the plasma density appears significantly enhanced. Model details agree well with recent broad-scale implications of satellite observations
Inequalities for Moment Cones of Finite-Dimensional Representations
We give a general description of the moment cone associated with an arbitrary
finite-dimensional unitary representation of a compact, connected Lie group in
terms of finitely many linear inequalities. Our method is based on combining
differential-geometric arguments with a variant of Ressayre's notion of a
dominant pair. As applications, we obtain generalizations of Horn's
inequalities to arbitrary representations, new inequalities for the one-body
quantum marginal problem in physics, which concerns the asymptotic support of
the Kronecker coefficients of the symmetric group, and a geometric
interpretation of the Howe-Lee-Tan-Willenbring invariants for the tensor
product algebra.Comment: 42 pages, to appear in Journal of Symplectic Geometr
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