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 pg=0p_g=0

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