Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Plane sections of space curves in positive characteristic
Get PDFIt is known that if C is a curve of degree d ≥ 6 in P^3 over an algebraically closed field of characteristic 0 such that its plane section is contained in an irreducible conic, then C lies on a quadric surface. We show under which conditions this result holds also in positive characteristic
Separating sequences of 0-dimensional schemes
Get PDFIn two previous papers, we defined, for every projective, 0-dimensional, reduced scheme X, a set of numerical sequences, which turns out to be a refinement of the Hilbert function of X. Here, we extend that definition to the case of a scheme X not necessarily reduced; the aim is reached by replacing a point by its corresponding “separating ideal” in its coordinate ring. The numerical sequences are obtained by taking the degrees of the elements appearing in suitable sequences of separating ideals. These latter sequences are themselves a good tool in the search for subschemes of X not in general position
Nonisotrivial families over curves with fixed point free automorphisms
Get PDFWe construct for any smooth projective curve of genus q ≥ 2 with a fixed point free automorphism a nonisotrivial family of curves. Moreover we study the space of the modular curves and one of the parameters
Combinatorial aspects of nodal curves
Get PDFTo any nodal curve C one associates its degree class group, a combinatorial invariant which plays an important role in the compactification of the generalized Jacobian of C and in the construction of the Néron model of the Picard variety of families of curves having C as special fibre. In this paper we study this invariant.More precisely, we construct a family of graphs having cyclic degree class group and we provide a recursive formula for the cardinality of the degree class group of the members of the family. Moreover, we analyse the behaviour of the degree class group under standard geometrical operations on the curve, such as the blow up and the normalization of a node
Entropy approximation for the system of moment equations describing charge transport in semiconductors
Get PDFThe question of possibility to build additional entropy conservation law for the system of moment equations, which appear in mathematical modelling of the charge transport in semiconductors, is discussed
Trees with the same path-table
Get PDFAs a generalization of isomorphisms of graphs, we consider path-congruences, that is maps which preserve the number of paths of any length.We construct families of pairs of non-isomorphic trees with the same path-table
A generalized small model property for languages which force the infinity
Get PDFThis paper deals with formulas of set theory which force the infinity.For such formulas, we provide a technique to infer satisfiability from a finite assignment
A decision procedure for a sublanguage of set theory involving monotone additive and multiplicative functions, II. The multi-level case
Get PDFMLSS is a decidable sublanguage of set theory involving the predicates membership, set equality, set inclusion, and the operators union, intersection, set difference, and singleton.In this paper we extend MLSS with constructs for expressing monotonicity, additivity, and multiplicativity properties of set-to-set functions. We prove that the resulting language is decidable by reducing the problem of determining the satisfiability of its sentences to the problem of determining the satisfiability of sentences of MLSS.In addition, we show an interesting model theoretic property of MLSS, the singleton model property, upon which our decidability proof is based. Intuitively, the singleton model property states that if a formula is satisfiable, then it is satisfiable in a model whose non-empty Venn regions are singleton sets
Some open problems regarding the determination of a set from its covariogram
Get PDFWe present and discuss some open problems related to the determination of a set K from its covariogram, i.e. the function which provides the volumes of the intersections of K with all its possible translates
Sur l\u27inégalité de Lewy-Stampacchia pour le problème bilatéral et pour le problème quadratique
Get PDFIn this paper, we present two results that we recently proved in [18] and [19]: on the first hand, the Lewy-Stampacchia’s inequality for the bilateral obstacle problem with a fairly general Leray-Lions operator; on the second hand, again the Lewy-Stampacchia’s inequality but now for the unilateral obstacle problem with a quasilinear operator perturbed by a non linearity with quadratic growth in the gradient