669 research outputs found
Quartic double solids with ordinary singularities
We study the mixed Hodge structure on the third homology group of a threefold
which is the double cover of projective three-space ramified over a quartic
surface with a double conic. We deal with the Torelli problem for such
threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7
Homological Type of Geometric Transitions
The present paper gives an account and quantifies the change in topology
induced by small and type II geometric transitions, by introducing the notion
of the \emph{homological type} of a geometric transition. The obtained results
agree with, and go further than, most results and estimates, given to date by
several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark
3.2 were added. This is the final version accepted for publication in the
journal Geometriae Dedicat
2-elementary subgroups of the space Cremona group
We give a sharp bound for orders of elementary abelian 2-groups of birational
automorphisms of rationally connected threefolds
Poisson-de Rham homology of hypertoric varieties and nilpotent cones
We prove a conjecture of Etingof and the second author for hypertoric
varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is
isomorphic to the de Rham cohomology of its hypertoric resolution. More
generally, we prove that this conjecture holds for an arbitrary conical variety
admitting a symplectic resolution if and only if it holds in degree zero for
all normal slices to symplectic leaves.
The Poisson-de Rham homology of a Poisson cone inherits a second grading. In
the hypertoric case, we compute the resulting 2-variable Poisson-de
Rham-Poincare polynomial, and prove that it is equal to a specialization of an
enrichment of the Tutte polynomial of a matroid that was introduced by Denham.
We also compute this polynomial for S3-varieties of type A in terms of Kostka
polynomials, modulo a previous conjecture of the first author, and we give a
conjectural answer for nilpotent cones in arbitrary type, which we prove in
rank less than or equal to 2.Comment: 25 page
Quantum Monte Carlo study on speckle variation due to photorelaxation of ferroelectric clusters in paraelectric barium titanate
Time-dependent speckle pattern of paraelectric barium titanate observed in a
soft x-ray laser pump-probe measurement is theoretically investigated as a
correlated optical response to the pump and probe pulses. The scattering
probability is calculated based on a model with coupled soft x-ray photon and
ferroelectric phonon mode. It is found that the speckle variation is related
with the relaxation dynamics of ferroelectric clusters created by the pump
pulse. Additionally, critical slowing down of cluster relaxation arises on
decreasing temperature towards the paraelectric-ferroelectric transition
temperature. Relation between critical slowing down, local dipole fluctuation
and crystal structure are revealed by quantum Monte Carlo simulation.Comment: 9 pages, 8 figure
Extending Torelli map to toroidal compactifications of Siegel space
It has been known since the 1970s that the Torelli map ,
associating to a smooth curve its jacobian, extends to a regular map from the
Deligne-Mumford compactification to the 2nd Voronoi
compactification .
We prove that the extended Torelli map to the perfect cone (1st Voronoi)
compactification is also regular, and moreover
and share a common Zariski open
neighborhood of the image of . We also show that the map to the
Igusa monoidal transform (central cone compactification) is NOT regular for
; this disproves a 1973 conjecture of Namikawa.Comment: To appear in Inventiones Mathematica
Probing early structure and model-independent neutrino mass with high-redshift CMB lensing mass maps
CMB lensing maps probe the mass distribution in projection out to high
redshifts, but significant sensitivity to low-redshift structure remains. In
this paper we discuss a method to remove the low-redshift contributions from
CMB lensing mass maps by subtracting suitably scaled galaxy density maps,
nulling the low redshift structure with a model-insensitive procedure that is
similar to delensing. This results in a high--only mass map that can provide
a probe of structure growth at uniquely high redshifts: if systematics can be
controlled, we forecast that CMB-S4 lensing combined with a Rubin-LSST-like
galaxy survey can probe the amplitude of structure at redshifts
() to within (). We then discuss other example applications
of such high- CMB lensing maps. In standard analyses of CMB lensing,
assuming the wrong dark energy model (or wrong model parametrization) can lead
to biases in neutrino mass constraints. In contrast, we show with forecasts
that a high- mass map constructed from CMB-S4 lensing and LSST galaxies can
provide a nearly model-independent neutrino mass constraint, with only
negligible sensitivity to the presence of non-standard dark energy models,
irrespective of their parametrization.Comment: 19 pages, 11 figure
Simple Lattice-Models of Ion Conduction: Counter Ion Model vs. Random Energy Model
The role of Coulomb interaction between the mobile particles in ionic
conductors is still under debate. To clarify this aspect we perform Monte Carlo
simulations on two simple lattice models (Counter Ion Model and Random Energy
Model) which contain Coulomb interaction between the positively charged mobile
particles, moving on a static disordered energy landscape. We find that the
nature of static disorder plays an important role if one wishes to explore the
impact of Coulomb interaction on the microscopic dynamics. This Coulomb type
interaction impedes the dynamics in the Random Energy Model, but enhances
dynamics in the Counter Ion Model in the relevant parameter range.Comment: To be published in Phys. Rev.
Position-Dependent Correlation Function of Weak Lensing Convergence
We provide a systematic study of the position-dependent correlation function
in weak lensing convergence maps and its relation to the squeezed limit of the
three-point correlation function (3PCF) using state-of-the-art numerical
simulations. We relate the position-dependent correlation function to its
harmonic counterpart, i.e., the position-dependent power spectrum or
equivalently the integrated bispectrum. We use a recently proposed improved
fitting function, BiHalofit, for the bispectrum to compute the theoretical
predictions as a function of source redshifts. In addition to low redshift
results () we also provide results for maps inferred from lensing
of the cosmic microwave background, i.e., . We include a {\em
Euclid}-type realistic survey mask and noise. In agreement with the recent
studies on the position-dependent power spectrum, we find that the results from
simulations are consistent with the theoretical expectations when appropriate
corrections are included.Comment: 7 pages, 7 figure
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