1,711 research outputs found
Smooth rationally connected threefolds contain all smooth curves
We show that if X is a smooth rationally connected threefold and C is a
smooth projective curve then C can be embedded in X. Furthermore, a version of
this property characterises rationally connected varieties of dimension at
least 3. We give some details about the toric case.Comment: Version 1 was called "Any smooth toric threefold contains all
curves". This version is completely rewritten and proves a much stronger
result, following suggestions of Janos Kolla
Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry
We develop a mathematical framework for the computation of open orbifold
Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with
predictions from open string mirror symmetry. To this aim we set up a
computation of open string invariants in the spirit of Katz-Liu, defining them
by localization. The orbifold is viewed as an open chart of a global quotient
of the resolved conifold, and the Lagrangian as the fixed locus of an
appropriate anti-holomorphic involution. We consider two main applications of
the formalism. After warming up with the simpler example of [C^3/Z_3], where we
verify physical predictions of Bouchard, Klemm, Marino and Pasquetti, the main
object of our study is the richer case of [C^3/Z_4], where two different
choices are allowed for the Lagrangian. For one choice, we make numerical
checks to confirm the B-model predictions; for the other, we prove a mirror
theorem for orbifold disc invariants, match a large number of annulus
invariants, and give mirror symmetry predictions for open string invariants of
genus \leq 2.Comment: 44 pages + appendices; v2: exposition improved, misprints corrected,
version to appear on Selecta Mathematica; v3: last minute mistake found and
fixed for the symmetric brane setup of [C^3/Z_4]; in pres
Seidel elements and mirror transformations
The goal of this article is to give a precise relation between the mirror
symmetry transformation of Givental and the Seidel elements for a smooth
projective toric variety with nef. We show that the Seidel elements
entirely determine the mirror transformation and mirror coordinates.Comment: 36 pages. We corrected several issues as pointed out by the refere
Prepotentials for local mirror symmetry via Calabi-Yau fourfolds
In this paper, we first derive an intrinsic definition of classical triple
intersection numbers of K_S, where S is a complex toric surface, and use this
to compute the extended Picard-Fuchs system of K_S of our previous paper,
without making use of the instanton expansion. We then extend this formalism to
local fourfolds K_X, where X is a complex 3-fold. As a result, we are able to
fix the prepotential of local Calabi-Yau threefolds K_S up to polynomial terms
of degree 2. We then outline methods of extending the procedure to non
canonical bundle cases.Comment: 42 pages, 7 figures. Expanded, reorganized, and added a theoretical
background for the calculation
The symplectic Deligne-Mumford stack associated to a stacky polytope
We discuss a symplectic counterpart of the theory of stacky fans. First, we
define a stacky polytope and construct the symplectic Deligne-Mumford stack
associated to the stacky polytope. Then we establish a relation between stacky
polytopes and stacky fans: the stack associated to a stacky polytope is
equivalent to the stack associated to a stacky fan if the stacky fan
corresponds to the stacky polytope.Comment: 20 pages; v2: To appear in Results in Mathematic
Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time
We present families of (hyper)elliptic curve which admit an efficient
deterministic encoding function
Orbit Determination with the two-body Integrals
We investigate a method to compute a finite set of preliminary orbits for
solar system bodies using the first integrals of the Kepler problem. This
method is thought for the applications to the modern sets of astrometric
observations, where often the information contained in the observations allows
only to compute, by interpolation, two angular positions of the observed body
and their time derivatives at a given epoch; we call this set of data
attributable. Given two attributables of the same body at two different epochs
we can use the energy and angular momentum integrals of the two-body problem to
write a system of polynomial equations for the topocentric distance and the
radial velocity at the two epochs. We define two different algorithms for the
computation of the solutions, based on different ways to perform elimination of
variables and obtain a univariate polynomial. Moreover we use the redundancy of
the data to test the hypothesis that two attributables belong to the same body
(linkage problem). It is also possible to compute a covariance matrix,
describing the uncertainty of the preliminary orbits which results from the
observation error statistics. The performance of this method has been
investigated by using a large set of simulated observations of the Pan-STARRS
project.Comment: 23 pages, 1 figur
Microwave properties of : Influence of magnetic scattering
We report measurements of the surface impedance of
, . Increasing
concentration leads to some striking results not observed in samples doped
by non-magnetic constituents. The three principal features of the data
- multiple structure in the transition, a high residual resistance and, at high
concentrations, an upturn of the low data, are all characteristic of
the influence of magnetic scattering on superconductivity, and appear to be
common to materials where magnetism and superconductivity coexist. The low
behavior of appears to change from to at large
doping, and provides evidence of the influence of magnetic pairbreaking of the
.Comment: 5 pages, 3 eps figures, Revtex, 2-column format, uses graphicx. To
appear in Physica C. Postscript version also available at
http://sagar.physics.neu.edu/preprints.htm
M-theory on `toric' G_2 cones and its type II reduction
We analyze a class of conical G_2 metrics admitting two commuting isometries,
together with a certain one-parameter family of G_2 deformations which
preserves these symmetries. Upon using recent results of Calderbank and
Pedersen, we write down the explicit G_2 metric for the most general member of
this family and extract the IIA reduction of M-theory on such backgrounds, as
well as its type IIB dual. By studying the asymptotics of type II fields around
the relevant loci, we confirm the interpretation of such backgrounds in terms
of localized IIA 6-branes and delocalized IIB 5-branes. In particular, we find
explicit, general expressions for the string coupling and R-R/NS-NS forms in
the vicinity of these objects. Our solutions contain and generalize the field
configurations relevant for certain models considered in recent work of Acharya
and Witten.Comment: 45 pages, references adde
Self-similar stable processes arising from high-density limits of occupation times of particle systems
We extend results on time-rescaled occupation time fluctuation limits of the
-branching particle system with Poisson initial condition. The earlier results in the homogeneous case
(i.e., with Lebesgue initial intensity measure) were obtained for dimensions
only, since the particle system becomes locally extinct if
. In this paper we show that by introducing high density
of the initial Poisson configuration, limits are obtained for all dimensions,
and they coincide with the previous ones if . We also give
high-density limits for the systems with finite intensity measures (without
high density no limits exist in this case due to extinction); the results are
different and harder to obtain due to the non-invariance of the measure for the
particle motion. In both cases, i.e., Lebesgue and finite intensity measures,
for low dimensions ( and
, respectively) the limits are determined by
non-L\'evy self-similar stable processes. For the corresponding high dimensions
the limits are qualitatively different: -valued L\'evy
processes in the Lebesgue case, stable processes constant in time on
in the finite measure case. For high dimensions, the laws of all
limit processes are expressed in terms of Riesz potentials. If , the
limits are Gaussian. Limits are also given for particle systems without
branching, which yields in particular weighted fractional Brownian motions in
low dimensions. The results are obtained in the setup of weak convergence of
S'(R^d)$-valued processes.Comment: 28 page
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