Some remarks on homogeneous K\"ahler manifolds

In this paper we provide a positive answer to a conjecture due to A. J. Di Scala, A. Loi, H. Hishi (see [3, Conjecture 1]) claiming that a simply-connected homogeneous K\"ahler manifold M endowed with an integral K\"ahler form $\mu\omega$, admits a holomorphic isometric immersion in the complex projective space, for a suitable $\mu>0$. This result has two corollaries which extend to homogeneous K\"ahler manifolds the results obtained by the authors in [8] and in [12] for homogeneous bounded domains.Comment: 8 page

Partially Isometric Immersions and Free Maps

In this paper we investigate the existence of ``partially'' isometric immersions. These are maps f:M->R^q which, for a given Riemannian manifold M, are isometries on some sub-bundle H of TM. The concept of free maps, which is essential in the Nash--Gromov theory of isometric immersions, is replaced here by that of H-free maps, i.e. maps whose restriction to H is free. We prove, under suitable conditions on the dimension q of the Euclidean space, that H-free maps are generic and we provide, for the smallest possible value of q, explicit expressions for H-free maps in the following three settings: 1-dimensional distributions in R^2, Lagrangian distributions of completely integrable systems, Hamiltonian distributions of a particular kind of Poisson Bracket.Comment: 19 pages, 1 figur

K\"ahler immersions of K\"ahler-Ricci solitons into definite or indefinite complex space forms

Let $(g, X)$ be a K\"ahler-Ricci soliton on a complex manifold $M$. We prove that if the K\"ahler manifold $(M, g)$ can be K\"ahler immersed into a definite or indefinite complex space form of constant holomorphic sectional curvature $2c$, then $g$ is Einstein. Moreover, its Einstein constant is a rational multiple of $c$

Preliminari alla ricomposizione dell’opera omnia di Antonio Simon Mossa: le fonti bibliografiche e l’archivio di famiglia

Il ritrovamento, nel 2007, dell’archivio personale di Antonio Simon Mossa ha aperto la strada a un approccio filologico verso una produzione assai più vasta di quanto generalmente ritenuto. Il confronto in atto tra il materiale restituito dall’archivio e la relativamente scarsa bibliografia finora edita si sta rivelando, a lavori ancora in corso, fondamentale punto di partenza per la ricomposizione di un’opera ampia, eclettica, estremamente frazionata e dispersa in una miriade di fonti, molte delle quali ancora da esplorare

LivDet 2017 Fingerprint Liveness Detection Competition 2017

Fingerprint Presentation Attack Detection (FPAD) deals with distinguishing images coming from artificial replicas of the fingerprint characteristic, made up of materials like silicone, gelatine or latex, and images coming from alive fingerprints. Images are captured by modern scanners, typically relying on solid-state or optical technologies. Since from 2009, the Fingerprint Liveness Detection Competition (LivDet) aims to assess the performance of the state-of-the-art algorithms according to a rigorous experimental protocol and, at the same time, a simple overview of the basic achievements. The competition is open to all academics research centers and all companies that work in this field. The positive, increasing trend of the participants number, which supports the success of this initiative, is confirmed even this year: 17 algorithms were submitted to the competition, with a larger involvement of companies and academies. This means that the topic is relevant for both sides, and points out that a lot of work must be done in terms of fundamental and applied research.Comment: presented at ICB 201

Balanced metrics on homogeneous vector bundles

Let $E\rightarrow M$ be a holomorphic vector bundle over a compact Kaehler manifold $(M, \omega)$ and let $E=E_1\oplus... \oplus E_m\rightarrow M$ be its decomposition into irreducible factors. Suppose that each $E_j$ admits a $\omega$-balanced metric in Donaldson-Wang terminology. In this paper we prove that $E$ admits a unique $\omega$-balanced metric if and only if $\frac{r_j}{N_j}=\frac{r_k}{N_k}$ for all $j, k=1, ..., m$, where $r_j$ denotes the rank of $E_j$ and $N_j=\dim H^0(M, E_j)$. We apply our result to the case of homogeneous vector bundles over a rational homogeneous variety $(M, \omega)$ and we show the existence and rigidity of balanced Kaehler embedding from $(M, \omega)$ into Grassmannians.Comment: 5 page

Dieci partigiani ossesi nella Resistenza italiana

La ricostruzione delle vicende biografiche dei dieci partigiani originari di Ossi finora identificati, riproponendo implicitamente il tema del rapporto fra vicissitudini individuali ed eventi storici, si inserisce nel più ampio contesto del contributo della ricerca locale e settoriale alla storiografia della Resistenza. In tal senso l’articolo, sintesi introduttiva di una monografia in corso di pubblicazione, si propone come ulteriore tassello nel quadro degli studi tuttora in corso sul contributo dei sardi alla guerra di Liberazione