Search results for "Geometria"

Automorphisms of Hyperelliptic GAG-codes

2008

In this talk, we discuss the n-automorphism groups of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such groups are, up to isomorphism, subgroups of the automorphism groups of the underlying function fields. We also present some examples in which the n-automorphism groups can be determined explicitly.

Splittings of Toric Ideals

2019

Let $I \subseteq R = \mathbb{K}[x_1,\ldots,x_n]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric ideals. For a general toric ideal $I$, we give a sufficient condition for this splitting in terms of the integer matrix that defines $I$. When $I = I_G$ is the toric ideal of a finite simple graph $G$, we give additional splittings of $I_G$ related to subgraphs of $G$. When there exists a splitting $I = I_1+I_2$ of the toric ideal, we show that in some cases we can describe the (multi-)graded Betti numbers of $I$ in terms of the (multi-)graded Betti numbers of $I_1$ and $I_2$.

On the representations in GF(3)^4 of the Hadamard design H_11

2020

In this paper we study the representations of the 2-(11,5,2) Hadamard design H_11 = (P,B) as a set of eleven points in the 4-dimensional vector space GF(3)^4, under the conditions that the five points in each block sum up to zero, and dim ‹P› = 4. We show that, up to linear automorphism, there exist precisely two distinct, linearly nonisomorphic representations, and, in either case, we characterize the family S of all the 5-subsets of P whose elements sum up to zero. In both cases, S properly contains the family of blocks B, thereby showing that a previous result on the representations of H_11 in GF(3)^5 cannot be improved.

Bounded Geometry, Growth and Topology

2011

Infinitesimal Hilbertianity of Locally CAT(κ)-Spaces

2021

We show that, given a metric space (Y,d)(Y,d) of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure μμ on YY giving finite mass to bounded sets, the resulting metric measure space (Y,d,μ)(Y,d,μ) is infinitesimally Hilbertian, i.e. the Sobolev space W1,2(Y,d,μ)W1,2(Y,d,μ) is a Hilbert space. The result is obtained by constructing an isometric embedding of the ‘abstract and analytical’ space of derivations into the ‘concrete and geometrical’ bundle whose fibre at x∈Yx∈Y is the tangent cone at x of YY. The conclusion then follows from the fact that for every x∈Yx∈Y such a cone is a CAT(0)CAT(0) space and, as such, has a Hilbert-like structure. peerReviewed

Calibrations and isoperimetric profiles

2007

We equip many noncompact nonsimply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly nongeneric property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new results on the profile of surfaces of revolution and some hardware know-how.

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.

Cardinal inequalities involving the Hausdorff pseudocharacter

2023

We establish several bounds on the cardinality of a topological space involving the Hausdorff pseudocharacter $H\psi(X)$. This invariant has the property $\psi_c(X)\leq H\psi(X)\leq\chi(X)$ for a Hausdorff space $X$. We show the cardinality of a Hausdorff space $X$ is bounded by $2^{pwL_c(X)H\psi(X)}$, where $pwL_c(X)\leq L(X)$ and $pwL_c(X)\leq c(X)$. This generalizes results of Bella and Spadaro, as well as Hodel. We show additionally that if $X$ is a Hausdorff linearly Lindel\"of space such that $H\psi(X)=\omega$, then $|X|\le 2^\omega$, under the assumption that either $2^{<\mathfrak{c}}=\mathfrak{c}$ or $\mathfrak{c}<\aleph_\omega$. The following game-theoretic result is shown: i…

Space of signatures as inverse limits of Carnot groups

2021

We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.…

Voisin's Conjecture for 0-cycles on Calabi-Yau varieties and their mirror

2019

We study a conjecture, due to Voisin, on 0-cycles on varieties with pg = 1. Using Kimura’s finite dimensional motives and recent results of Vial’s on the refined (Chow–)Künneth decomposition, we provide a general criterion for Calabi–Yau manifolds of dimension at most 5 to verify Voisin’s conjecture. We then check, using in most cases some cohomological computations on the mirror partners, that the criterion can be successfully applied to various examples in each dimension up to 5.