1,400 research outputs found
The modular variety of hyperelliptic curves of genus three
The modular variety of non singular and complete hyperelliptic curves with
level-two structure of genus 3 is a 5-dimensional quasi projective variety
which admits several standard compactifications. The first one, X, comes from
the realization of this variety as a sub-variety of the Siegel modular variety
of level two and genus three .We will be to describe the equations of X in a
suitable projective embedding and its Hilbert function. It will turn out that
X is normal. A further model comes from geometric invariant theory using
so-called semistable degenerated point configurations in (P^1)^8 . We denote
this GIT-compactification by Y. The equations of this variety in a suitable
projective embedding are known. This variety also can by identified with a
Baily-Borel compactified ball-quotient. We will describe these results in some
detail and obtain new proofs including some finer results for them. We have a
birational map between Y and X . In this paper we use the fact that there are
graded algebras (closely related to algebras of modular forms) A,B such that
X=proj(A) and Y=proj(B). This homomorphism rests on the theory of Thomae (19th
century), in which the thetanullwerte of hyperelliptic curves have been
computed. Using the explicit equations for we can compute the base locus
of the map from Y to X.
Blowing up the base locus and the singularity of Y, we get a dominant, smooth
model {\tilde Y}. We will see that {\tilde Y} is isomorphic to the
compactification of families of marked projective lines (P^1,x_1,...,x_8),
usually denoted by {\bar M_{0,8}}. There are several combinatorial similarities
between the models X and Y. These similarities can be described best, if one
uses the ball-model to describe Y.Comment: 39 page
Some Siegel threefolds with a Calabi-Yau model II
In the paper [FSM] we described some Siegel modular threefolds which admit a
Calabi-Yau model. Using a different method we give in this paper an enlarged
list of such varieties that admits a Calabi-Yau model in the following weak
sense: there exists a desingularization in the category of complex spaces of
the Satake compactification which admits a holomorphic three-form without zeros
and whose first Betti number vanishes Basic for our method is the paper [GN] of
van Geemen and Nygaard.Comment: 23 pages, no figure
Maine Indian rights the worst in the country
Does Michael L. Lane thoroughly research a subject before he use[s] his pen? Responding to All bets are off (Maine Campus Feb. 16), Lane has addressed four separate issues in one commentary. This is typical over-generalized […] when it comes to addressing Native American issues
Classical theta constants vs. lattice theta series, and super string partition functions
Recently, various possible expressions for the vacuum-to-vacuum superstring
amplitudes has been proposed at genus . To compare the different
proposals, here we will present a careful analysis of the comparison between
the two main technical tools adopted to realize the proposals: the classical
theta constants and the lattice theta series. We compute the relevant Fourier
coefficients in order to relate the two spaces. We will prove the equivalence
up to genus 4. In genus five we will show that the solutions are equivalent
modulo the Schottky form and coincide if we impose the vanishing of the
cosmological constant.Comment: 21 page
Spontaneous Pattern Formation in a Polariton Condensate
Polariton condensation can be regarded as a self-organization phenomenon,
where phase ordering is established among particles in the system. In such
condensed systems, further ordering can possibly occur in the particle density
distribution, under particular experimental conditions. In this work we report
on spontaneous pattern formation in a polariton condensate under non-resonant
optical pumping. The slightly elliptical ring-shaped excitation laser we employ
is such to force condensation to occur in a single-energy state with periodic
boundary conditions, giving rise to a multi-lobe standing wave patterned state
Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in -Li2IrO3: full solution via magnetic resonant x-ray diffraction
The recently-synthesized iridate -LiIrO has been proposed as a
candidate to display novel magnetic behavior stabilized by frustration effects
from bond-dependent, anisotropic interactions (Kitaev model) on a
three-dimensional "hyperhoneycomb" lattice. Here we report a combined study
using neutron powder diffraction and magnetic resonant x-ray diffraction to
solve the complete magnetic structure. We find a complex, incommensurate
magnetic order with non-coplanar and counter-rotating Ir moments, which
surprisingly shares many of its features with the related structural polytype
"stripyhoneycomb" -LiIrO, where dominant Kitaev interactions
have been invoked to explain the stability of the observed magnetic structure.
The similarities of behavior between those two structural polytypes, which have
different global lattice topologies but the same local connectivity, is
strongly suggestive that the same magnetic interactions and the same underlying
mechanism governs the stability of the magnetic order in both materials,
indicating that both - and -LiIrO are strong candidates
to realize dominant Kitaev interactions in a solid state material.Comment: 14 pages, 9 figure
Harmonic theta series and the kodaira dimension of a6
We construct a basis of the space S14(Sp12(ℤ)) of Siegel cusp forms of degree 6 and weight 14 consisting of harmonic theta series. One of these functions has vanishing order 2 at the boundary which implies that the Kodaira dimension of A6 is nonnegative
Penrose-Onsager Criterion Validation in a One-Dimensional Polariton Condensate
We perform quantum tomography on one-dimensional polariton condensates,
spontaneously occurring in linear disorder valleys in a CdTe planar microcavity
sample. By the use of optical interferometric techniques, we determine the
first-order coherence function and the amplitude and phase of the order
parameter of the condensate, providing a full reconstruction of the single
particle density matrix for the polariton system. The experimental data are
used as input to theoretically test the consistency of Penrose-Onsager
criterion for Bose-Einstein condensation in the framework of nonequilibrium
polariton condensates. The results confirm the pertinence and validity of the
criterion for a non equilibrium condensed gas.Comment: 5 pages, 4 figure
Spontaneous self-ordered states of vortex-antivortex pairs in a Polariton Condensate
Polariton condensates have proved to be model systems to investigate
topological defects, as they allow for direct and non-destructive imaging of
the condensate complex order parameter. The fundamental topological excitations
of such systems are quantized vortices. In specific configurations, further
ordering can bring the formation of vortex lattices. In this work we
demonstrate the spontaneous formation of ordered vortical states, consisting in
geometrically self-arranged vortex-antivortex pairs. A mean-field generalized
Gross-Pitaevskii model reproduces and supports the physics of the observed
phenomenology
Effect of isoelectronic doping on honeycomb lattice iridate A_2IrO_3
We have investigated experimentally and theoretically the series
(NaLi)IrO. Contrary to what has been believed so far,
only for the system forms uniform solid solutions. For larger Li
content, as evidenced by powder X-ray diffraction, scanning electron microscopy
and density functional theory calculations, the system shows a miscibility gap
and a phase separation into an ordered NaLiIrO phase with
alternating Na and LiIrO planes, and a Li-rich phase close to pure
LiIrO. For we observe (1) an increase of with Li
doping up to , despite the fact that in pure LiIrO is
smaller than in NaIrO, and (2) a gradual reduction of the
antiferromagnetic ordering temperature and ordered moment. The
previously proposed magnetic quantum phase transition at may
occur in a multiphase region and its nature needs to be re-evaluated.Comment: 8 pages, 9 figures including supplemental informatio
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