Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Euclid\u27s and Hilbert\u27s foundations of geometry
No full textThe purpose of this note is to substantiate and explain the following quote from Hilbert
On the proof of a minimax principle
Get PDFThe aim of this note is to point out that the basic argument in the proof of Theorem 2 in [5] does not work. Comments on this topic are given
A classification of tha plane similarity transformations
Get PDFGeometric transformations have been included in school programs since long now
A new model for the theta divisor of the cubic threefold
Get PDFIn this paper we give a birational model for the theta divisor of the intermediate Jacobian of a generic cubic threefold X . We use the standard realization of X as a conic bundle and a 4−dimensional family of plane quartics which are totally tangent to the discriminant quintic curve of such a conic bundle structure. The additional data of an even theta characteristic on the curves in the family gives us a model for the theta divisor
Geometrical properties of sections of Buchsbaum-Rim sheaves
Get PDFWe present a method for constructing arithmetically Gorenstein subschemes of P^n of large codimension using sections of so called Buchsbaum-Rim sheaves and implement it in the computer algebra system SINGULAR
Irreducibility of Hurwitz spaces of covering of an elliptic curve of prime degree with one point of total ramification
Get PDFLet Y be an elliptic curve, p a prime number and WH_{p,n}(Y) the Hurwitz space that parametrizes equivalence classes of p-sheeted branched coverings of Y , with n branch points, n − 1 of which are points of simple ramification and one of total ramification.In this paper, we prove that WH_{p,n}(Y) is irreducible if n − 1≥ 2 p
Some results on simple complete ideals having one characteristic pair
Get PDFLet α be a regular local two-dimensional ring, and let m = (x, y) be its maximal ideal. Let m > n > 1 be coprime integers, and let p be the integral closure of the ideal (x^m , y^n ). Then p is a simple complete m-primary ideal, and its value semigroup is generated by m, n.We construct a minimal system of generators {z_0 , . . . , z_n } of p, and from this we get a minimal system of generators of the polar ideal p\u27 of p, consisting of n = θ elements. In particular, we show that p and p\u27 are monomial ideals. When α = κ[ [ x, y ] ], a ring of formal power series over an algebraically closed field κ of characteristic zero, this implies the existence of some relevant property
Retraction of chaotic manifolds and fractal
Get PDFIn this article we will describe some types of retractions of chaotic manifold. We also will introduce a definition for the fractional dimension of the chaotic manifold. Some theorems related to them will be obtained. Some applications will also be mentioned in this paper
Hilbert e la teoria degli invarianti
No full textLa nascita della teoria degli invarianti viene attribuita a Lagrange e Gauss, ..
Gli studi sui fondamenti della geometria nella seconda metà dell\u27ottocento con particolare riferimento alla situazione italiana
No full textAppare immediato a chi si soffermi sulla storia della matematica della seconda metà dell\u27ottocento che lo studio della geometria ebbe in quel periodo notevoli sviluppi