Waldschmidt constants for Stanley-Reisner ideals of a class of graphs

In the present note we study Waldschmidt constants of Stanley-Reisner ideals of a hypergraph and a graph with vertices forming a bipyramid over a planar n-gon. The case of the hypergraph has been studied by Bocci and Franci. We reprove their main result. The case of the graph is new. Interestingly, both cases provide series of ideals with Waldschmidt constants descending to 1. It would be interesting to known if there are bounded ascending sequences of Waldschmidt constants.Comment: 7 pages, 2 figure

Osculating spaces to secant varieties

We generalize the classical Terracini's Lemma to higher order osculating spaces to secant varieties. As an application, we address with the so-called Horace method the case of the $d$-Veronese embedding of the projective 3-space

The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

The m−m-dissimilarity map and representation theory of SLmSL_m

We give another proof that $m$-dissimilarity vectors of weighted trees are points on the tropical Grassmanian, as conjectured by Cools, and proved by Giraldo in response to a question of Sturmfels and Pachter. We accomplish this by relating $m$-dissimilarity vectors to the representation theory of $SL_m.$Comment: 11 pages, 8 figure

Hadamard Products of Symbolic Powers and Hadamard Fat Grids

In this paper we address the question if, for points P, Q ? P-2, I(P)I-m(*)(Q)(n) = I(P(*)Q)(m+n-1 )and we obtain different results according to the number of zero coordinates in P and Q. Successively, we use our results to define the so called Hadamard fat grids, which are the result of the Hadamard product of two sets of collinear points with given multiplicities. The most important invariants of Hadamard fat grids, as minimal resolution, Waldschmidt constant and resurgence, are then computed

Interspecific and Intraspecific Artificial Insemination in Domestic Equids

Simple Summary Among equids, the mule (jackass stallion x mare) is the most common hybrid, followed by the hinny (horse stallion x jenny). This study describes the outcome of inseminating mares and jennies with either fresh horse or donkey semen of proven fertility. Pregnancy rates in horse females were significantly higher than in donkey females, while horse and donkey males did not affect pregnancy rates. Overall, intraspecific pregnancy rates were significantly higher than interspecific ones. Horses and donkeys differ phenotypically and karyotypically, although they can interbreed freely. Eight Standardbred mares and nine Amiata donkey jennies were included in the study. Semen was collected from two horses and two donkey stallions of proven fertility. A first pregnancy diagnosis was performed on day 10 after ovulation and repeated every day until embryo detection or until day 16. Irrespectively of the sire species, pregnancy rates in horse females (20/30, 66.7%) were significantly higher than in donkey females (19/70, 27.1%) (p < 0.05), while horse and donkey males did not affect pregnancy rates. Comparing overall intraspecific and interspecific AI, pregnancy rates were 25/37 (67.6%) and 14/63 (22.2%), respectively (p = 0.0001). The lowest pregnancy rate was obtained when inseminating jennies with horse stallion semen (8/49, 16.3%). No statistical differences were found when comparing embryo diameters, day at first pregnancy diagnosis, or in vitro embryo morphological quality among groups. In this study, much poorer results were obtained with jennies than with mares. Interspecific AI resulted in lower pregnancy rates than intraspecific Al, and AI to produce hinny hybrids resulted in the lowest pregnancy rate. Further studies are required to better understand the mechanism involved in such different outcomes in relation to intra- and interspecific breeding in domestic equids

Performance of upstream interaction region detectors for the FIRST experiment at GSI

The FIRST (Fragmentation of Ions Relevant for Space and Therapy) experiment at GSI has been designed to study carbon fragmentation, measuring 12C double differential cross sections (∂2σ/ ∂θ∂E) for different beam energies between 100 and 1000 MeV/u. The experimental setup integrates newly designed detectors in the, so called, Interaction Region around the graphite target. The Interaction Region upstream detectors are a 250 μm thick scintillator and a drift chamber optimized for a precise measurement of the ions interaction time and position on the target. In this article we review the design of the upstream detectors along with the preliminary results of the data taking performed on August 2011 with 400 MeV/u fully stripped carbon ion beam at GSI. Detectors performances will be reviewed and compared to those obtained during preliminary tests, performed with 500 MeV electrons (at the BTF facility in the INFN Frascati Laboratories) and 80 MeV/u protons and carbon ions (at the INFN LNS Laboratories in Catania)

On the dimensions of secant varieties of Segre-Veronese varieties

This paper explores the dimensions of higher secant varieties to Segre-Veronese varieties. The main goal of this paper is to introduce two different inductive techniques. These techniques enable one to reduce the computation of the dimension of the secant variety in a high dimensional case to the computation of the dimensions of secant varieties in low dimensional cases. As an application of these inductive approaches, we will prove non-defectivity of secant varieties of certain two-factor Segre-Veronese varieties. We also use these methods to give a complete classification of defective s-th Segre-Veronese varieties for small s. In the final section, we propose a conjecture about defective two-factor Segre-Veronese varieties.Comment: Revised version. To appear in Annali di Matematica Pura e Applicat