Search results for " geometria"

A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms

2017

Abstract The realification of the ( 2 n + 1 ) -dimensional complex Heisenberg Lie algebra is a ( 4 n + 2 ) -dimensional real nilpotent Lie algebra with a 2-dimensional commutator ideal coinciding with the centre, and admitting the compact algebra sp ( n ) of derivations. We investigate, in general, whether a real nilpotent Lie algebra with 2-dimensional commutator ideal coinciding with the centre admits a compact Lie algebra of derivations. This also gives us the occasion to revisit a series of classic results, with the expressed aim of attracting the interest of a broader audience.

A note on rank 2 diagonals

2020

<p>We solve two questions regarding spaces with a (G<sub>δ</sub>)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos about weakly Lindelöf spaces with a G<sub>δ</sub>-diagonal of rank 2 and the other is a question of Arhangel’skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.</p>

On GIT quotients of Hilbert and Chow schemes of curves

2011

The aim of this note is to announce some results on the GIT problem for the Hilbert and Chow scheme of curves of degree d and genus g in P^{d-g}, whose full details will appear in a subsequent paper. In particular, we extend the previous results of L. Caporaso up to d>4(2g-2) and we observe that this is sharp. In the range 2(2g-2)<d<7/2(2g-2), we get a complete new description of the GIT quotient. As a corollary, we get a new compactification of the universal Jacobian over the moduli space of pseudo-stable curves.

MR 3219513 Reviewed Venkataramana T. N. Monodromy of cyclic coverings of the projective line. Invent. Math., 197 (2014), 1–-45. (Reviewer Francesca V…

2014

Let $d \geq 2$ and $n \geq 1$ be integers and $P_{n+1}$ be the pure braid group on $n + 1$ strands. In this paper, the author studies the image of $P_{n+1}$ under the monodromy action on the homology of a cyclic covering of degree $d$ of the projective line. More precisely, let $k_{1}, \ldots, k_{n + 1}$ be integers such that $1 \leq k_{i} \leq d - 1$ and gcd$(k_{i}, d) = 1$ for each $i$. Moreover, let $a_{1}, \ldots, a_{n + 1}$ be distinct points of the complex plane and $C$ be the space of points in $\mathbb{C}^{n + 1}$ with all distinct coordinates. Let us denote by $X_{a, k}$ the affine curve defined by the equation $$ y^{d} = (x - a_{1})^{k_{1}} (x - a_{2})^{k_{2}} \cdots (x - a_{n +1}…

Multiplicative loops of 2-dimensional topological quasifields

2015

We determine the algebraic structure of the multiplicative loops for locally compact $2$-dimensional topological connected quasifields. In particular, our attention turns to multiplicative loops which have either a normal subloop of positive dimension or which contain a $1$-dimensional compact subgroup. In the last section we determine explicitly the quasifields which coordinatize locally compact translation planes of dimension $4$ admitting an at least $7$-dimensional Lie group as collineation group.

The generalized commutativity degree in a finite group

2009

Geometria e architettura militare

2007

The essay highlights the growing diffusion of treaties relating to the military architecture in Sicily since the second half of the sixteenth century. The research carried out by analyzing the inventories of wills of the Sicilian architects of the seventeenth and eighteenth centuries, the library catalog '"Biscari "and the inventories related to the libraries of some religious orders, revealed an unusually large presence of international treaties related to the mathematical sciences and its applications in the field of architecture both civic and military (geometry, perspective, optics). The research has allowed to reconstruct in part the library of some prestigious architects such as Paolo…

Gδ covers of compact spaces

2018

We solve a long standing question due to Arhangel'skii by constructing a compact space which has a Gδ cover with no continuum-sized (Gδ)-dense subcollection. We also prove that in a countably compact weakly Lindelöf normal space of countable tightness, every Gδ cover has a -sized subcollection with a Gδ-dense union and that in a Lindelöf space with a base of multiplicity continuum, every Gδ cover has a continuum sized subcover. We finally apply our results to obtain a bound on the cardinality of homogeneous spaces which refines De La Vega's celebrated theorem on the cardinality of homogeneous compacta of countable tightness.

Unirationality of Hurwitz spaces of coverings of degree <= 5

2011

Let $Y$ be a smooth, projective curve of genus $g\geq 1$ over the complex numbers. Let $H^0_{d,A}(Y)$ be the Hurwitz space which parametrizes coverings $p:X \to Y$ of degree $d$, simply branched in $n=2e$ points, with monodromy group equal to $S_d$, and $det(p_{*}O_X/O_Y)$ isomorphic to a fixed line bundle $A^{-1}$ of degree $-e$. We prove that, when $d=3, 4$ or $5$ and $n$ is sufficiently large (precise bounds are given), these Hurwitz spaces are unirational. If in addition $(e,2)=1$ (when $d=3$), $(e,6)=1$ (when $d=4$) and $(e,10)=1$ (when $d=5$), then these Hurwitz spaces are rational.

On the geometry of S2

2009

We investigate topological properties of the moduli space of spin structures over genus two curves. In particular, we provide a combinatorial description of this space and give a presentation of the (rational) cohomology ring via generators and relations.