Search results for "Geometria"

On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces

2017

We study the arithmetically Cohen-Macaulay (ACM) property for finite sets of points in multiprojective spaces, especially ( P 1 ) n (\mathbb P^1)^n . A combinatorial characterization, the ( ⋆ ) (\star ) -property, is known in P 1 × P 1 \mathbb P^1 \times \mathbb P^1 . We propose a combinatorial property, ( ⋆ s ) (\star _s) with 2 ≤ s ≤ n 2\leq s\leq n , that directly generalizes the ( ⋆ ) (\star ) -property to ( P 1 ) n (\mathbb P^1)^n for larger n n . We show that X X is ACM if and only if it satisfies the ( ⋆ n ) (\star _n) -property. The main tool for several of our results is an extension to the multiprojective setting of certain liaison methods in projective space.

Elementary (-1)-curves of P-3

2006

In this note we deal with rational curves in P^3 which are images of a line by means of a finite sequence of cubo-cubic Cremona transformations. We prove that these curves can always be obtained applying to the line a sequence of such transformations increasing at each step the degree of the curve. As a corollary we get a result about curves that can give speciality for linear systems of P^3.

Counting and equidistribution in quaternionic Heisenberg groups

2020

AbstractWe develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

L'azione del gruppo simplettico associata ad un'estensione quadratica di campi

2000

Given a quadratic extension L/K of fields and a regular alternating space (V; f) of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group Sp_L(V; f) in the set of K-subspaces of V.

Solvable Extensions of Nilpotent Complex Lie Algebras of Type {2n,1,1}

2018

We investigate derivations of nilpotent complex Lie algebras of type {2n, 1, 1} with the aim to classify nilpotent complex Lie algebras the commutator ideals of which have codimension one and are nilpotent Lie algebras of type {2n, 1, 1}

Skeleta of affine hypersurfaces

2014

A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation of its Newton polytope, we provide a purely combinatorial construction of a compact topological space S as a union of components of real dimension n, and prove that S embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S.

Intrinsic rectifiability via flat cones in the Heisenberg group

2022

We give a geometric criterion for a topological surface in the first Heisenberg group to be an intrinsic Lipschitz graph, using planar cones instead of the usual open cones. peerReviewed

Extending an example by Colding and Minicozzi

2018

Extending an example by Colding and Minicozzi, we construct a sequence of properly embedded minimal disks $\Sigma_i$ in an infinite Euclidean cylinder around the $x_3$-axis with curvature blow-up at a single point. The sequence converges to a non smooth and non proper minimal lamination in the cylinder. Moreover, we show that the disks $\Sigma_i$ are not properly embedded in a sequence of open subsets of $\mathbb{ R}^3$ that exhausts $\mathbb{ R}^3$.

The nonabelian tensor product of two soluble minimax groups

2010

Restituzioni omografiche di finte cupole: la cupola di Santa Maria dei Rimedi a Palermo

2016

Nel vasto repertorio siciliano delle prospettive solide, un ruolo di spicco è ricoperto da un esempio unico di realizzazione di finta prospettiva di cupola sferica su copertura ad arco ribassato, ricavata sull’incrocio del transetto con la navata centrale nella chiesa di Santa Maria dei Rimedi a Palermo. L’unicità di quest’opera sta nella geometria reale della cupola ribassata. Infatti gli esempi più diffusi di finte cupole in Sicilia sono realizzati su soffitti piani lignei o in calcestruzzo. In Appendice 1 si potrà consultare il repertorio delle finte cupole esistenti in Sicilia per la cui stesura ci si è avvalsi degli studi condotti dall’architetto Giuseppe Ingaglio nell’ambito della sua…