Curves with Canonical Models on Scrolls

Let $C$ be an integral and projective curve whose canonical model $C'$ lies on a rational normal scroll $S$ of dimension $n$. We mainly study some properties on $C$, such as gonality and the kind of singularities, in the case where $n=2$ and $C$ is non-Gorenstein, and in the case where $n=3$, the scroll $S$ is smooth, and $C'$ is a local complete intersection inside $S$. We also prove that a rational monomial curve with just one singular point lies on a surface scroll if and only if its gonality is at most $3$, and that it lies on a threefold scroll if and only if its gonality is at most $4$

On the Singular Scheme of Split Foliations

We prove that the tangent sheaf of a codimension one locally free distribution splits as a sum of line bundles if and only if its singular scheme is arithmetically Cohen-Macaulay. In addition, we show that a foliation by curves is given by an intersection of generically transversal holomorphic distributions of codimension one if and only if its singular scheme is arithmetically Buchsbaum. Finally, we establish that these foliations are determined by their singular schemes, and deduce that the Hilbert scheme of certain arithmetically Buchsbaum schemes of codimension $2$ is birational to a Grassmannian.Comment: 21 page

Polynomial ring representations of endomorphisms of exterior powers

A polynomial ring with rational coefficients is an irreducible representation of Lie algebras of endomorphisms of exterior powers of a infinite countable dimensional $\mathbb{Q}$-vector space. We give an explicit description of it, using suitable vertex operators on exterior algebras, which mimick those occurring in the bosonic vertex representation of the Lie algebra $gl_\infty$, due to Date--Jimbo--Kashiwara and Miwa (DJKM).Comment: few typos corrected, references updated, comments are very welcom

Data Management in the APPA System

International audienceCombining Grid and P2P technologies can be exploited to provide high-level data sharing in large-scale distributed environments. However, this combination must deal with two hard problems: the scale of the network and the dynamic behavior of the nodes. In this paper, we present our solution in APPA (Atlas Peer-to-Peer Architecture), a data management system with high-level services for building large-scale distributed applications. We focus on data availability and data discovery which are two main requirements for implementing large-scale Grids. We have validated APPA's services through a combination of experimentation over Grid5000, which is a very large Grid experimental platform, and simulation using SimJava. The results show very good performance in terms of communication cost and response time