Ideals of general forms and the ubiquity of the Weak Lefschetz property

Let $d_1,...,d_r$ be positive integers and let $I = (F_1,...,F_r)$ be an ideal generated by general forms of degrees $d_1,...,d_r$, respectively, in a polynomial ring $R$ with $n$ variables. When all the degrees are the same we give a result that says, roughly, that they have as few first syzygies as possible. In the general case, the Hilbert function of $R/I$ has been conjectured by Fr\"oberg. In a previous work the authors showed that in many situations the minimal free resolution of $R/I$ must have redundant terms which are not forced by Koszul (first or higher) syzygies among the $F_i$ (and hence could not be predicted from the Hilbert function), but the only examples came when $r=n+1$. Our second main set of results in this paper show that further examples can be obtained when $n+1 \leq r \leq 2n-2$. We also show that if Fr\"oberg's conjecture on the Hilbert function is true then any such redundant terms in the minimal free resolution must occur in the top two possible degrees of the free module. Related to the Fr\"oberg conjecture is the notion of Weak Lefschetz property. We continue the description of the ubiquity of this property. We show that any ideal of general forms in $k[x_1,x_2,x_3,x_4]$ has it. Then we show that for certain choices of degrees, any complete intersection has it and any almost complete intersection has it. Finally, we show that most of the time Artinian ``hypersurface sections'' of zeroschemes have it.Comment: 24 page

Cationic ordering control of magnetization in Sr2FeMoO6 double perovskite

The role of the synthesis conditions on the cationic Fe/Mo ordering in Sr2FeMoO6 double perovskite is addressed. It is shown that this ordering can be controlled and varied systematically. The Fe/Mo ordering has a profound impact on the saturation magnetization of the material. Using the appropriate synthesis protocol a record value of 3.7muB/f.u. has been obtained. Mossbauer analysis reveals the existence of two distinguishable Fe sites in agreement with the P4/mmm symmetry and a charge density at the Fe(m+) ions significantly larger than (+3) suggesting a Fe contribution to the spin-down conduction band. The implications of these findings for the synthesis of Sr2FeMoO6 having optimal magnetoresistance response are discussed.Comment: 9 pages, 4 figure

On the shape of a pure O-sequence

An order ideal is a finite poset X of (monic) monomials such that, whenever M is in X and N divides M, then N is in X. If all, say t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h=(1,h_1,...,h_e), counting the monomials of X in each degree. Equivalently, in the language of commutative algebra, pure O-sequences are the h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of Richard Stanley's early works in this area, and have since played a significant role in at least three disciplines: the study of simplicial complexes and their f-vectors, level algebras, and matroids. This monograph is intended to be the first systematic study of the theory of pure O-sequences. Our work, making an extensive use of algebraic and combinatorial techniques, includes: (i) A characterization of the first half of a pure O-sequence, which gives the exact converse to an algebraic g-theorem of Hausel; (ii) A study of (the failing of) the unimodality property; (iii) The problem of enumerating pure O-sequences, including a proof that almost all O-sequences are pure, and the asymptotic enumeration of socle degree 3 pure O-sequences of type t; (iv) The Interval Conjecture for Pure O-sequences (ICP), which represents perhaps the strongest possible structural result short of an (impossible?) characterization; (v) A pithy connection of the ICP with Stanley's matroid h-vector conjecture; (vi) A specific study of pure O-sequences of type 2, including a proof of the Weak Lefschetz Property in codimension 3 in characteristic zero. As a corollary, pure O-sequences of codimension 3 and type 2 are unimodal (over any field); (vii) An analysis of the extent to which the Weak and Strong Lefschetz Properties can fail for monomial algebras; (viii) Some observations about pure f-vectors, an important special case of pure O-sequences.Comment: iii + 77 pages monograph, to appear as an AMS Memoir. Several, mostly minor revisions with respect to last year's versio

Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type

In this paper we show a partial answer the a question of C. Huneke and G. Leuschke (2003): Let R be a standard graded Cohen-Macaulay ring of graded countable Cohen-Macaulay representation type, and assume that R has an isolated singularity. Is R then necessarily of graded finite Cohen-Macaulay representation type? In particular, this question has an affirmative answer for standard graded non-Gorenstein rings as well as for standard graded Gorenstein rings of minimal multiplicity. Along the way, we obtain a partial classification of graded Cohen-Macaulay rings of graded countable Cohen-Macaulay type.Comment: 15 Page

Hadron structure in tau -> KKpi nu_tau decays

We analyse the hadronization structure of both vector and axial-vector currents leading to tau -> KKpi nu_tau decays. At leading order in the 1/Nc expansion, and considering only the contribution of the lightest resonances, we work out, within the framework of the resonance chiral Lagrangian, the structure of the local vertices involved in those processes. The couplings in the resonance theory are constrained by imposing the asymptotic behaviour of vector and axial-vector spectral functions ruled by QCD. In this way we predict the hadron spectra and conclude that, contrarily to previous assertions, the vector contribution dominates by far over the axial-vector one in all KKpi charge channels.Comment: 32 pages, 7 figure

The first confirmation of V-type asteroids among the Mars crosser population

The Mars crossing region constitutes a path to deliver asteroids from the Inner Main Belt to the Earth crossing space. While both the Inner Main Belt and the population of Earth crossing asteroids contains a significant fraction of asteroids belonging to the V taxonomic class, only two of such V-type asteroids has been detected in the Mars crossing region up to now. In this work, we searched for asteroids belonging to the V class among the population of Mars crossing asteroids, in order to support alternative paths to the delivery of this bodies into the Earth crossing region. We selected 18 candidate V-type asteroids in the Mars crossing region using observations contained in the Sloan Digital Sky Survey Moving Objects Catalog. Then, we observed 4 of these candidates to take their visible spectra using the Southern Astrophysical Research Telescope (SOAR). We also performed the numerical simulation of the orbital evolution of the observed asteroids. We confirmed that 3 of the observed asteroids belong to the V class, and one of these may follow a path that drives it to an Earth collision in some tens of million years

Extended Riemann-Liouville type fractional derivative operator with applications

The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presentedThe research of J.J. Nieto has been partially supported by the Ministerio de Economía y Competitividad of Spain under grants MTM2016–75140–P, MTM2013–43014–P, Xunta de Galicia, Grants GRC2015-004 and R2016-022, and co- nanced by the European Community fund FEDERS

Corona-Australis DANCe I. Revisiting the census of stars with Gaia-DR2 data

Context. Corona-Australis is one of the nearest regions to the Sun with recent and ongoing star formation, but the current picture of its stellar (and substellar) content is not complete yet. Aims. We take advantage of the second data release of the Gaia space mission to revisit the stellar census and search for additional members of the young stellar association in Corona-Australis. Methods. We applied a probabilistic method to infer membership probabilities based on a multidimensional astrometric and photometric data set over a field of 128 deg(2) around the dark clouds of the region. Results. We identify 313 high-probability candidate members to the Corona-Australis association, 262 of which had never been reported as members before. Our sample of members covers the magnitude range between G greater than or similar to 5 mag and G less than or similar to 20 mag, and it reveals the existence of two kinematically and spatially distinct subgroups. There is a distributed "off-cloud" population of stars located in the north of the dark clouds that is twice as numerous as the historically known "on-cloud" population that is concentrated around the densest cores. By comparing the location of the stars in the HR-diagram with evolutionary models, we show that these two populations are younger than 10 Myr. Based on their infrared excess emission, we identify 28 Class II and 215 Class III stars among the sources with available infrared photometry, and we conclude that the frequency of Class II stars (i.e. "disc-bearing" stars) in the on-cloud region is twice as large as compared to the off-cloud population. The distance derived for the Corona-Australis region based on this updated census is d = 149.4(-0.4)(+0.4) pc, which exceeds previous estimates by about 20 pc. Conclusions. In this paper we provide the most complete census of stars in Corona-Australis available to date that can be confirmed with Gaia data. Furthermore, we report on the discovery of an extended and more evolved population of young stars beyond the region of the dark clouds, which was extensively surveyed in the past