4,550 research outputs found
Quotients of the square of a curve by a mixed action, further quotients and Albanese morphisms
We study mixed surfaces, the minimal resolution S of the singularities of a
quotient (C x C)/G of the "square" of a curve by a finite group G of
automorphisms that contains elements not preserving the factors. We study them
through the "further quotients" by (C x C)/G' where G' contains G.
As a first application we prove that if the irregularity is at least 3, then
S is also minimal. The result is sharp.
The main result is a complete description of the Albanese morphism of S
through a determined further quotient (C x C)/G' that is an \'etale cover of
the symmetric square of a curve. In particular, if the irregularity of S is at
least 2, then S has maximal Albanese dimension.
We apply our result to all the "semi-isogenous" mixed surfaces of maximal
Albanese dimension constructed by Cancian and Frapporti, relating them with the
other constructions appearing in the literature of surfaces of general type
having the same invariants.Comment: 18 pages, final version to appear on Rev. Mat. Complu
Multi-component models for disk galaxies. A test case on NGC 5866
We present an application of a new set of detailed, self-consistent,
dynamical models for disc galaxies. We start from the hypothesis that each
galaxy can be decomposed in a bulge, following the r^{1/4} law, and a disc with
an exponential projected density profile; and that the isodensity surfaces of
each component can be represented by similar concentric spheroids. After taking
into account both the asymmetric drift effects and the integration along the
line of sight, we produce the rotational velocity and velocity dispersion
profile,_and_ the approximate shape of the line of sight velocity distributions
for the stars as parameterized by the h3 and h4 coefficients of the
Gauss-Hermite expansion of the line profile.
Photometric and kinematical data have been taken from the literature for the
test case of the S0 galaxy NGC 5866, for which detailed stellar kinematical
data are available at different positions across the galaxy. Apart from the
very inner, dust-obscured regions of the galaxy, where observational effects
are likely to be dominant, the model successfully reproduce the whole set of
dynamical data available as well as giving a good fit to the photometry. The
galaxy is shown to have an isotropic velocity dispersion tensor, thus giving a
hint on a dissipational formation process.Comment: 8 pages, 6 encapsulated figures, requires kluwer.sty. To appear in:
J.E. Beckman (ed.) "The Evolution of Galaxies on Cosmological Timescale",
Proceedings of the meeting held at Puerto de la Cruz (Spain) on November
30-December 5, 199
A Massive Dark Object in the S0 galaxy NGC 4350
We present a new detection of a Massive Dark Object in the S0 Galaxy NGC
4350, obtained applying a new dynamical model on ground-based photometric and
kinematic data already present in literature.Comment: 2 pages, 2 figures. Proceedings of the conference "Galaxy Disks and
Disk Galaxies", ASP Conference Series, J.G Funes, S.J and E.M. Corsini, ed
Dynamical Models Of S0 And Sa Galaxies
We present a set of detailed, self-consistent, isotropic dynamical models for
disc galaxies. We start from the hypothesis that each galaxy can be decomposed
in a bulge, following the r^{1/4} law, and a disc with an exponential projected
density profile; and that the isodensity surfaces of each component can be
represented by similar concentric spheroids. Under these conditions we produce
the rotational velocity and velocity dispersion profiles, after taking into
account both the asymmetric drift effects and the integration along the line of
sight. The model is successfully applied to reproduce the stellar kinematic and
photometry of the bulge of the 4 lenticular and early-type spiral galaxies NGC
4565, NGC 7814, NGC 5866 and NGC 4594. For these galaxies detailed stellar
kinematical data are available at different positions across the galaxy. The
application of our models shows that: 1) For all the galaxies considered in
this work, an isotropic model is able to reproduce the whole dynamical data.
This is surprising in the special case of NGC 4565, for which previous models
were unable to reproduce the velocity distribution without introducing strong
anisotropies. 2) We do not need a dark mass halo to reproduce these data. This
do not mean that a dark halo is not present, but just that its dynamical
effects in these inner regions of the galaxies are negligible.Comment: To appear in "Dark and Visible Matter in Galaxies and Cosmological
Implications," eds. M. Persic and P. Salucci, A.S.P. Conference Series.8
pages, 5 encapsulated postscript figures, LaTex, requires paspconf.sty and
epsf.st
Anatomy of giant spiral galaxies
We present B and I band photometry, gas and star kinematics and 3D modelling
of 7 giant spiral galaxies. The stellar systems studied have morphological
types spanning from S0/a to Sc and absolute magnitudes from -20.6 to -22.5.
The spectra have been collected with the spectrographs Boller & Chivens and
EFOSC2 of the 2.2m ESO-MPI telescope. Images have been taken with the same
telescope.
The models fit simultaneously the photometric and kinematics data using a
disk+bulge tridimensional model. The distribution of luminous matter, coming
from the fit of the photometric data is compared with the distribution of total
matter derived from the velocity dispersion and velocity curves.
The intrinsic properties of these galaxies, such as the disk/bulge mass
ratio, the total mass and the scale length of the galaxy components are
presented and discussed.Comment: 2 pages, 2 figures, proceedings of the Conference "Galaxy Disk and
Disk Galaxies" held in Rome, June 12-16, 200
Unprojection and deformations of tertiary Burniat surfaces
We construct a 4-dimensional family of surfaces of general type with p_g=0
and K^2=3 and fundamental group Z/2xQ_8, where Q_8 is the quaternion group. The
family constructed contains the Burniat surfaces with K^2=3. Additionally, we
construct the universal coverings of the surfaces in our family as complete
intersections on (\PP^1)^4 and we also give an action of Z/2xQ_8 on (\PP^1)^4
lifting the natural action on the surfaces.
The strategy is the following. We consider an \'etale (Z/2)^3-cover T of a
surface with p_g=0 and K^2=3 and assume that it may be embedded in a Fano
3-fold V. We construct V by using the theory of parallel unprojection. Since V
is an Enriques--Fano 3-fold, considering its Fano cover yields the simple
description of the universal covers above.Comment: 29 pages, 3 figures. Final version. To appear in Ann. Scuola Norm.
Sup. Pisa Cl. Sc
The classification of minimal product-quotient surfaces with
A product-quotient surface is the minimal resolution of the singularities of
the quotient of a product of two curves by the action of a finite group acting
separately on the two factors. We classify all minimal product-quotient
surfaces of general type with geometric genus 0: they form 72 families. We show
that there is exactly one product-quotient surface of general type with big
canonical class which is not minimal, and describe its (-1) curves. For all
these surfaces the Bloch conjecture holds.Comment: 59 pages. v2: exposition improve
Surfaces with K^2=8, p_g=4 and canonical involution
In this paper we classify completely all regular minimal surfaces with K^2=8,
p_g=4 whose canonical map is composed with an involution. We obtain six
unirational families of respective dimensions 28,28,32,33,38,34. The last two
are irreducible components of the moduli space of minimal surfaces with K^2=8,
p_g=4. These families hit three different topological types.Comment: 23 pages. In this version we correct an error (which does not change
the main theorem) and simplify substantially some proofs. For sake of clarity
we decided to be more detailed in the case of surfaces having a genus 2
penci
Mixed quasi-\'etale quotients with arbitrary singularities
A mixed quasi-\'etale quotient is the quotient of the product of a curve of
genus at least 2 with itself by the action of a group which exchanges the two
factors and acts freely out of a finite subset. A mixed quasi-\'etale surface
is the minimal resolution of its singularities.
We produce an algorithm computing all mixed quasi-\'etale surfaces with given
geometric genus, irregularity, and self-intersection of the canonical class. We
prove that all irregular mixed quasi-\'etale surfaces of general type are
minimal.
As application, we classify all irregular mixed quasi \'etale surfaces of
general type with genus equal to the irregularity, and all the regular ones
with K^2>0, thus constructing new examples of surfaces of general type with
\chi=1. We mention the first example of a minimal surface of general type with
p_g=q=1 and Albanese fibre of genus bigger than K^2.Comment: 27 pages; v2: minor corrections, to be published in Glasgow
Mathematical Journa
Symbolic template iterations of complex quadratic maps
The behavior of orbits for iterated logistic maps has been widely studied
since the dawn of discrete dynamics as a research field, in particular in the
context of the complex quadratic family. However, little is is known about
orbit behavior if the map changes along with the iterations. We investigate in
which ways the traditional theory of Fatou-Julia may still apply in this case,
illustrating how the iteration pattern (symbolic template) can affect the
topology of the Julia and Mandelbrot sets.
We briefly discuss the potential of this extension towards a variety of
applications in genetic and neural coding, since it investigates how an
occasional or a reoccurring error in a replication or learning algorithm may
affect the dynamic outcome.Comment: 18 pages, 12 figures, 2 appendice
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