Families of determinantal schemes

Given integers a_0 \le a_1 \le ... \le a_{t+c-2} and b_1 \le ... \le b_t, we denote by W(b;a) \subset Hilb^p(\PP^{n}) the locus of good determinantal schemes X \subset \PP^{n} of codimension c defined by the maximal minors of a t x (t+c-1) homogeneous matrix with entries homogeneous polynomials of degree a_j-b_i. The goal of this short note is to extend and complete the results given by the authors in [10] and determine under weakened numerical assumptions the dimension of W(b;a), as well as whether the closure of W(b;a) is a generically smooth irreducible component of the Hilbert scheme Hilb^p(\PP^{n}).Comment: The non-emptiness of W(b;a) is restated as (2.2) in this version; the codimension c=2 case in (2.5)-(2.6) is reconsidered, and c > 2 (c > 3) is now an assumption in (2.16)-(2.17). 13 page

Ideals generated by submaximal minors

The goal of this paper is to study irreducible families W(b;a) of codimension 4, arithmetically Gorenstein schemes X of P^n defined by the submaximal minors of a t x t matrix A with entries homogeneous forms of degree a_j-b_i. Under some numerical assumption on a_j and b_i we prove that the closure of W(b;a) is an irreducible component of Hilb^{p(x)}(P^n), we show that Hilb^{p(x)}(P^n) is generically smooth along W(b;a) and we compute the dimension of W(b;a) in terms of a_j and b_i. To achieve these results we first prove that X is determined by a regular section of the twisted conormal sheaf I_Y/I^2_Y(s) where s=deg(det(A)) and Y is a codimension 2, arithmetically Cohen-Macaulay scheme of P^n defined by the maximal minors of the matrix obtained deleting a suitable row of A.Comment: 22 page

Neutron capture reactions on Lu isotopes at DANCE

The DANCE (Detector for Advanced Neutron Capture Experiments) array located at the Los Alamos national laboratory has been used to obtain the neutron capture cross sections for 175Lu and 176Lu with neutron energies from thermal up to 100 keV. Both isotopes are of current interest for the nucleosynthesis s-process in astrophysics and for applications as in reactor physics or in nuclear medicine. Three targets were used to perform these measurements. One was natLu foil and the other two were isotope-enriched targets of 175Lu and 176Lu. The cross sections are obtained for now through a precise neutron flux determination and a normalization at the thermal neutron cross section value. A comparison with the recent experimental data and the evaluated data of ENDF/B-VII.0 will be presented. In addition, resonances parameters and spin assignments for some resonances will be featured

MC generator TAUOLA: implementation of Resonance Chiral Theory for two and three meson modes. Comparison with experiment

We present a partial upgrade of the Monte Carlo event generator TAUOLA with the two and three hadron decay modes using the theoretical models based on Resonance Chiral Theory. These modes account for 88% of total hadronic width of the tau meson. First results of the model parameters have been obtained using BaBar data for three pion mode.Comment: 5 pages, 1 figure, contribution to the Proceedings of the QCD@Work12 Conferenc

Theoretical inputs and errors in the new hadronic currents in TAUOLA

The new hadronic currents implemented in the TAUOLA library are obtained in the unified and consistent framework of Resonance Chiral Theory: a Lagrangian approach in which the resonances exchanged in the hadronic tau decays are active degrees of freedom included in a way that reproduces the low-energy results of Chiral Perturbation Theory. The short-distance QCD constraints on the imaginary part of the spin-one correlators yield relations among the couplings that render the theory predictive. In this communication, the obtaining of the two- and three-meson form factors is sketched. One of the criticisms to our framework is that the error may be as large as 1/3, since it is a realization of the large-N_C limit of QCD in a meson theory. A number of arguments are given which disfavor that claim pointing to smaller errors, which would explain the phenomenological success of our description in these decays. Finally, other minor sources of error and current improvements of the code are discussed.Comment: 5 pages, no figures, contribution to the Proceedings of the QCD@Work12 Conferenc

Moduli spaces of reflexive sheaves of rank 2

Let \sF be a coherent rank 2 sheaf on a scheme Y \subset \proj{n} of dimension at least two. In this paper we study the relationship between the functor which deforms a pair (\sF,\sigma), \sigma \in H^0(\sF), and the functor which deforms the corresponding pair (X,\xi) given as in the Serre correspondence. We prove that the scheme structure of e.g. the moduli scheme M_Y(P) of stable sheaves on a threefold Y at (\sF), and the scheme structure at (X) of the Hilbert scheme of curves on Y are closely related. Using this relationship we get criteria for the dimension and smoothness of M_Y(P) at (\sF), without assuming Ext^2(\sF,\sF) = 0. For reflexive sheaves on Y = \proj{3} whose deficiency module M = H_{*}^1(\sF) satisfies Ext^2(M,M) = 0 in degree zero (e.g. of diameter at most 2), we get necessary and sufficient conditions of unobstructedness which coincide in the diameter one case. The conditions are further equivalent to the vanishing of certain graded Betti numbers of the free graded minimal resolution of H_{*}^0(\sF). It follows that every irreducible component of M_{\proj{3}}(P) containing a reflexive sheaf of diameter one is reduced (generically smooth). We also determine a good lower bound for the dimension of any component of M_{\proj{3}}(P) which contains a reflexive stable sheaf with "small" deficiency module M.Comment: 19 page

Taxonomy of asteroid families among the Jupiter Trojans: Comparison between spectroscopic data and the Sloan Digital Sky Survey colors

We present a comparative analysis of the spectral slope and color distributions of Jupiter Trojans, with particular attention to asteroid families. We use a sample of data from the Moving Object Catalogue of the Sloan Digital Sky Survey, together with spectra obtained from several surveys. A first sample of 349 observations, corresponding to 250 Trojan asteroids, were extracted from the Sloan Digital Sky Survey, and we also extracted from the literature a second sample of 91 spectra, corresponding to 71 Trojans. The spectral slopes were computed by means of a least-squares fit to a straight line of the fluxes obtained from the Sloan observations in the first sample, and of the rebinned spectra in the second sample. In both cases the reflectance fluxes/spectra were renormalized to 1 at 6230 $\textrm{\AA}$. We found that the distribution of spectral slopes among Trojan asteroids shows a bimodality. About 2/3 of the objects have reddish slopes compatible with D-type asteroids, while the remaining bodies show less reddish colors compatible with the P-type and C-type classifications. The members of asteroid families also show a bimodal distribution with a very slight predominance of D-type asteroids, but the background is clearly dominated by the D-types. The L4 and L5 swarms show different distributions of spectral slopes, and bimodality is only observed in L4. These differences can be attributed to the asteroid families since the backgraound asteroids show the same slope distribtuions in both swarms. The analysis of individual families indicates that the families in L5 are taxonomically homogeneous, but in L4 they show a mixture of taxonomic types. We discuss a few scenarios that might help to interpret these results.Comment: 20 pages, 15 figures, 2 table