24,042 research outputs found
On Zariski's theorem in positive characteristic
In the current paper we show that the dimension of a family of
irreducible reduced curves in a given ample linear system on a toric surface
over an algebraically closed field is bounded from above by
, where denotes a general curve in the family. This result
generalizes a famous theorem of Zariski to the case of positive characteristic.
We also explore new phenomena that occur in positive characteristic: We show
that the equality does not imply the nodality of
even if belongs to the smooth locus of , and construct reducible Severi
varieties on weighted projective planes in positive characteristic,
parameterizing irreducible reduced curves of given geometric genus in a given
ample linear system.Comment: 19 pages. Several typos have been fixed, and a couple of examples and
pictures have been added. To appear in JEM
Natural Neutrino Dark Energy
A new class of neutrino dark energy models is presented. The new models are
characterized by the lack of exotic particles or couplings that violate the
standard model symmetry. It is shown that these models lead to several concrete
predictions for the dark energy equation of state, as well as possible effects
on the cosmic structure formation. These predictions, can be verified (or
disproved) with future experiments. At this point, the strongest constraints on
these models are obtained from big bang nucleosynthesis, and lead to new bounds
on the mass of the lightest neutrino.Comment: 14 pages, 6 figure
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