177,400 research outputs found
On the Gorenstein locus of some punctual Hilbert schemes
No full textLet be an algebraically closed field and let \Hilb_{d}^{G}(\p{N}) be the open locus of the Hilbert scheme \Hilb_{d}(\p{N}) corresponding to Gorenstein subschemes. We prove that \Hilb_{d}^{G}(\p{N}) is irreducible for . Moreover we also give a complete picture of its singular locus in the same range . Such a description of the singularities gives some evidence to a conjecture on the nature of the singular points in \Hilb_{d}^{G}(\p{N}) that we state at the end of the pape
Remarks on degree 4 projective curves
No full textIn this paper we characterize the degree 4 multiple lines with generic embedding dimension 3 and among them the ones with very degenerate hyperplanc section, and the ones which contain a degree 3 planar subcurve. Using that characterization, we prove that the degree 4 curves containing a planar subcurve of degree 3 are the general element of all irreducible component of the Hilbert scheme. Moreover, we show that all the multiple lines we consider belong to the same connected component of the corresponding Hilbert scheme
Cosmological parameter estimation: impact of CMB aberration
No full textThe peculiar motion of an observer with respect to the CMB rest frame induces an apparent deflection of the observed CMB photons, i.e. aberration, and a shift in their frequency, i.e. Doppler effect. Both effects distort the temperature multipoles a(l)m's via a mixing matrix at any l. The common lore when performing a CMB based cosmological parameter estimation is to consider that Doppler affects only the l = 1 multipole, and neglect any other corrections. In this paper we reconsider the validity of this assumption, showing that it is actually not robust when sky cuts are included to model CMB foreground contaminations. Assuming a simple fiducial cosmological model with five parameters, we simulated CMB temperature maps of the sky in a WMAP-like and in a Planck-like experiment and added aberration and Doppler effects to the maps. We then analyzed with a MCMC in a Bayesian framework the maps with and without aberration and Doppler effects in order to assess the ability of reconstructing the parameters of the fiducial model. We find that, depending on the specific realization of the simulated data, the parameters can be biased up to one standard deviation for WMAP and almost two standard deviations for Planck. Therefore we conclude that in general it is not a solid assumption to neglect aberration in a CMB based cosmological parameter estimation
On curves of P^n with extremal Hartshorne-Rao module in positive degrees
No full textAbstractIn this paper, we study the curves C in Pn, of degree d and genus g, with extremal Rao function in positive degrees, and non degenerate general hyperplane section. We describe their total ideal and various properties of the generators of the ideal. Moreover, we characterize these curves as intersection of two aCM curves of maximal genus whose union in aCM of maximal genus, and we completely describe the Rao function of these curves in negative degrees, too
Replicated measurements and algebraic statistics
No full textA basic application of algebraic statistics to design and analysis of experiments considers a design as a zero-dimensional variety and identifies it with the ideal of the variety. Then, a subset of a standard basis of the design ideal is used as support for identifiable regression models. Estimation of the model parameter is performed by standard least squares techniques. We consider this identifiability problem in the case where more than one measurement is taken at a design point
On the description and identifiability analysis of experiments with mixtures
No full textIn a mixture experiment the collinearity problems, implied by the sum to one functional relationship among the factors, have strong consequences on the identification and analysis of regression models for such designs. Here to address these problems, mixture designs are represented as sets of homogeneous polynomials. Techniques from computational commutative algebra are employed to deduce generalized confounding relationships on power products, and to determine families of identifiable models
Non-Gaussianity and CMB aberration and Doppler
No full textThe peculiar motion of an observer with respect to the CMB rest frame induces a deflection in the arrival direction of the observed photons (also known as CMB aberration) and a Doppler shift in the measured photon frequencies. As a consequence, aberration and Doppler effects induce non trivial correlations between the harmonic coefficients of the observed CMB temperature maps. In this paper we investigate whether these correlations generate a bias on non-Gaussianity estimators fNL. We perform this analysis simulating a large number of temperature maps with Planck-like resolution (lmax = 2000) as different realizations of the same cosmological fiducial model (WMAP7yr). We then add to these maps aberration and Doppler effects employing a modified version of the HEALPix code. We finally evaluate a generalization of the Komatsu, Spergel and Wandelt non-Gaussianity estimator for all the simulated maps, both when peculiar velocity effects have been considered and when these phenomena have been neglected. Using the value v/c = 1.23 × 10−3 for our peculiar velocity, we found that the aberration/Doppler induced non-Gaussian signal is at most of about half of the cosmic variance σ for fNL both in a full-sky and in a cut-sky experimental configuration, for local, equilateral and orthogonal estimators. We conclude therefore that when estimating fNL it is safe to ignore aberration and Doppler effects if the primordial map is already Gaussian. More work is necessary however to assess whether a map which contains non-Gaussianity can be significantly distorted by a peculiar velocity
Inflation from the Higgs field false vacuum with hybrid potential
No full textWe have recently suggested that Inflation could have started in a local minimum of the Higgs potential at field values of about 10^15−10^17 GeV, which exists for a narrow band of values of the top quark and Higgs masses and thus gives rise to a prediction on the Higgs mass to be in the range 123-129 GeV, together with a prediction on the the top mass and the cosmological tensor-to-scalar ratio r. Inflation can be achieved provided there is an additional degree of freedom which allows the transition to a radiation era. In [1] we had proposed such field to be a Brans-Dicke scalar. Here we present an alternative possibility with an additional subdominant scalar very weakly coupled to the Higgs, realizing an (inverted) hybrid Inflation scenario. Interestingly, we show that such model has an additional constraint mH<125.3±3th, where 3th is the present theoretical uncertainty on the Standard Model RGEs. The tensor-to-scalar ratio has to be within the narrow range 10−4≲r<0.007, and values of the scalar spectral index compatible with the observed range can be obtained. Moreover, if we impose the model to have subplanckian field excursion, this selects a narrower range 10−4≲r<0.001 and an upper bound on the Higgs mass of about mH<124±3th
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