Search results for " Mathematica"

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.

PreGarside monoids and groups, parabolicity, amalgamation, and FC property

2012

We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin–Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the notion of parabolic subgroup, we prove that any preGarside group has a (partial) complemented presentation, and we characterize the parabolic subgroups in terms of these presentations. Afterwards we prove that the amalgamated product of two preGarside groups along a common parabolic subgroup is again a preGarside group. This enables us to define the family of preGarside groups of FC type as the smallest family of preGarside groups that contains the Garside g…

Vehicles PEMFC Power System Mathematical Model for Integrated Design

2013

Measurement of visible cross sections in proton-lead collisions at √sNN= 5.02 TeV in van der Meer scans with the ALICE detector

2014

In 2013, the Large Hadron Collider provided proton-lead and lead-proton collisions at the center-of-mass energy per nucleon pair $\sqrt{s_{\rm{NN}}}=5.02$ TeV. Van der Meer scans were performed for both configurations of colliding beams, and the cross section was measured for two reference processes, based on particle detection by the T0 and V0 detectors, with pseudo-rapidity coverage $4.6<\eta< 4.9$, $-3.3<\eta<-3.0$ and $2.8<\eta< 5.1$, $-3.7<\eta<-1.7$, respectively. Given the asymmetric detector acceptance, the cross section was measured separately for the two configurations. The measured visible cross sections are used to calculate the integrated luminosity of the proton-lead and lead-…

On the exponent of mutually permutable products of two abelian groups

2016

In this paper we obtain some bounds for the exponent of a finite group, and its derived subgroup, which is a mutually permutable product of two abelian subgroups. They improve the ones known for products of finite abelian groups, and they are used to derive some interesting structural properties of such products.

$$O_2(\mathbb {C})$$O2(C)-Vector Bundles and Equivariant Real Circle Actions

2020

The main goal of this article is to give an expository overview of some new results on real circle actions on affine four-space and their relation to previous results on \(O_2(\mathbb {C})\)-equivariant vector bundles. In Moser-Jauslin (Infinite families of inequivalent real circle actions on affine four-space, 2019, [13]), we described infinite families of equivariant real circle actions on affine four-space. In the present note, we will describe how these examples were constructed, and some consequences of these results.

Analyticity of a restricted formality

2020

International audience; The Kontsevich formality can be viewed as a non-linear map ℱ from the L∞ algebra of poly-vector fields on ℝd to the space of poly-differential operators. The space of the half-homogenous poly-vector fields is a sub-L∞ algebra. We prove here that the restriction of ℱto this subspace is weakly analytic.

Relative cohomology spaces for some osp($n|2$)-modules

2018

International audience; In this work, we describe the H-invariant, so(n)-relative cohomology of a natural class of osp(n|2)-modules M, for n ≠ 2. The Lie superalgebra osp(n|2) can be realized as a superalgebra of vector fields on the superline R1|n. This yields canonical actions on spaces of densities and differential operators on the superline. The above result gives the zero, first, and second cohomology spaces for these modules of densities and differential operators.

Ulrich bundles on K3 surfaces

2019

We show that any polarized K3 surface supports special Ulrich bundles of rank 2.

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.