On the intersection of ACM curves in \PP^3

Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in P^3 never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in P^3. The bound that we give is in many cases optimal as a function of only the degrees and the initial degrees of the curves

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

Cohomological characterization of vector bundles on multiprojective spaces

We show that Horrock's criterion for the splitting of vector bundles on \PP^n can be extended to vector bundles on multiprojective spaces and to smooth projective varieties with the weak CM property (see Definition 3.11). As a main tool we use the theory of $n$-blocks and Beilinson's type spectral sequences. Cohomological characterizations of vector bundles are also showed

Existence of Rank Two Vector Bundles on Higher Dimensional Toric Varieties

In the mid 70's, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on P^n is a direct sum of line bundles. This conjecture remains still open. In this paper, we construct indecomposable rank two vector bundles on a large class of Fano toric varieties. Unfortunately, this class does not contain P^nComment: 8 page

Geometric collections and Castelnuovo-Mumford Regularity

The paper begins by overviewing the basic facts on geometric exceptional collections. Then, we derive, for any coherent sheaf \cF on a smooth projective variety with a geometric collection, two spectral sequences: the first one abuts to \cF and the second one to its cohomology. The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on smooth projective varieties $X$ with a geometric collection $\sigma$. We define the notion of regularity of a coherent sheaf \cF on $X$ with respect to $\sigma$. We show that the basic formal properties of the Castelnuovo-Mumford regularity of coherent sheaves over projective spaces continue to hold in this new setting and we show that in case of coherent sheaves on \PP^n and for a suitable geometric collection of coherent sheaves on \PP^n both notions of regularity coincide. Finally, we carefully study the regularity of coherent sheaves on a smooth quadric hypersurface Q_n \subset \PP^{n+1} ($n$ odd) with respect to a suitable geometric collection and we compare it with the Castelnuovo-Mumford regularity of their extension by zero in \PP^{n+1}.Comment: To appear in Math. Proc. Cambridg

Efecto del envejecimiento y de la temperatura en el comportamiento a fatiga de las mezclas bituminosas

The ageing of asphalt mixes, together with their exposure to low temperatures, causes a progressive increase of cracking. In this paper, the effect of ageing and temperature on the fatigue of asphalt concretes made with two types of binders, conventional (50/70) and polymer modified bitumen (PMB), is studied. For this purpose, specimens previously subjected to an accelerated laboratory ageing process were tested by a strain sweep test at different temperatures (-5ºC, 5ºC and 20°C). Results were compared with the obtained from the unaged specimens showing the relative importance of ageing, temperature and type of bitumen on the parameters that determine the fatigue life of the mixture. The mixtures behaviour becomes more brittle with ageing and the decrease of temperature. However, ageing hardly has an effect on fatigue at lower temperatures. In general, mixtures made with polymer modified bitumen have a better fatigue performance to ageing and temperature.El envejecimiento de las mezclas, unido a su exposición a bajas temperaturas, provoca un progresivo aumento de su fisuración. En este trabajo, se estudia el efecto del envejecimiento y la temperatura en la fatiga de una mezcla semidensa fabricada con dos tipos de ligantes, 50/70 y PMB 45/80-65. Para ello, probetas previamente sometidas a envejecimiento acelerado en laboratorio fueron ensayadas mediante un ensayo de barrido de deformaciones, a diferentes temperaturas (-5, 5 y 20ºC). Los resultados fueron comparados con los obtenidos en mezclas no envejecidas mostrando la importancia del envejecimiento, temperatura y ligante sobre los parámetros que condicionan la vida a fatiga de la mezcla. El comportamiento de las mezclas es más frágil debido al envejecimiento y la disminución de la temperatura. Sin embargo, el envejecimiento apenas influye en la fatiga a temperaturas bajas. En general, las mezclas con betún modificado muestran mejor respuesta a fatiga frente a envejecimiento y temperatura