THE DAIRY POLICY OF THE EUROPEAN COMMUNITY

Agricultural and Food Policy,

When the positivity of the h-vector implies the Cohen-Macaulay property

We study relations between the Cohen-Macaulay property and the positivity of $h$-vectors, showing that these two conditions are equivalent for those locally Cohen-Macaulay equidimensional closed projective subschemes $X$, which are close to a complete intersection $Y$ (of the same codimension) in terms of the difference between the degrees. More precisely, let $X\subset \mathbb P^n_K$ ($n\geq 4$) be contained in $Y$, either of codimension two with $deg(Y)-deg(X)\leq 5$ or of codimension $\geq 3$ with $deg(Y)-deg(X)\leq 3$. Over a field $K$ of characteristic 0, we prove that $X$ is arithmetically Cohen-Macaulay if and only if its $h$-vector is positive, improving results of a previous work. We show that this equivalence holds also for space curves $C$ with $deg(Y)-deg(C)\leq 5$ in every characteristic $ch(K)\neq 2$. Moreover, we find other classes of subschemes for which the positivity of the $h$-vector implies the Cohen-Macaulay property and provide several examples.Comment: Main changes with respect the previuos version are in the title, the abstract, the introduction and the bibliograph

Functors of Liftings of Projective Schemes

A classical approach to investigate a closed projective scheme $W$ consists of considering a general hyperplane section of $W$, which inherits many properties of $W$. The inverse problem that consists in finding a scheme $W$ starting from a possible hyperplane section $Y$ is called a {\em lifting problem}, and every such scheme $W$ is called a {\em lifting} of $Y$. Investigations in this topic can produce methods to obtain schemes with specific properties. For example, any smooth point for $Y$ is smooth also for $W$. We characterize all the liftings of $Y$ with a given Hilbert polynomial by a parameter scheme that is obtained by gluing suitable affine open subschemes in a Hilbert scheme and is described through the functor it represents. We use constructive methods from Gr\"obner and marked bases theories. Furthermore, by classical tools we obtain an analogous result for equidimensional liftings. Examples of explicit computations are provided.Comment: 25 pages. Final version. Ancillary files available at http://wpage.unina.it/cioffifr/MaterialeCoCoALiftingGeometric

Spatial price dynamics in the EU F&V sector: the cases of tomato and cauliflower

The paper explores the characteristics of spatial price dynamics for fresh vegetables. The analysis is carried out on selected EU prices for tomatoes and cauliflowers collected on some of the main production and consumption markets. It is based on the estimation of an time-varying threshold autoregressive econometric specification that is shown capable to underline the asymmetries in inter-Countries price transmission. The model shows that that horizontal price transmissions among net producer and net consumer markets is asymmetric and how such characteristic differs for markets closer to production areas or to consumption locations. This paper allowed to assess the average elapsing time for shocks to be transmitted among spatially separated markets, and, in particular, it shows the speed of transmission of price raises and price falls.price transmission, TVECM, vegetables, Agribusiness, Agricultural and Food Policy, Community/Rural/Urban Development, Food Consumption/Nutrition/Food Safety, Labor and Human Capital,

The price stabilization effects of the EU entry price scheme for fruits and vegetables

The paper assesses the stabilization effects of the EU import regime for fresh fruit and vegetables based on the entry price system. The analysis is carried out on the EU prices of tomatoes and lemons and those of imports from some of the main competing countries on the EU domestic markets: Morocco, Argentina and Turkey. It is based on the estimation of a threshold vector autoregressive econometric model that is shown capable of taking the workings of the import regime into account. The model shows that prices behave differently when import prices are above/below the trigger entry price. This paper allowed to highlight the cases for which the isolation effect of EPS seems reached and the resulting stabilization effects

A combinatorial description of finite O-sequences and aCM genera

The goal of this paper is to explicitly detect all the arithmetic genera of arithmetically Cohen-Macaulay projective curves with a given degree $d$. It is well-known that the arithmetic genus $g$ of a curve $C$ can be easily deduced from the $h$-vector of the curve; in the case where $C$ is arithmetically Cohen-Macaulay of degree $d$, $g$ must belong to the range of integers $\big\{0,\ldots,\binom{d-1}{2}\big\}$. We develop an algorithmic procedure that allows one to avoid constructing most of the possible $h$-vectors of $C$. The essential tools are a combinatorial description of the finite O-sequences of multiplicity $d$, and a sort of continuity result regarding the generation of the genera. The efficiency of our method is supported by computational evidence. As a consequence, we single out the minimal possible Castelnuovo-Mumford regularity of a curve with Cohen-Macaulay postulation and given degree and genus.Comment: Final versio