Fibers of Generic Projections

Let X be a smooth projective variety of dimension n in P^r. We study the fibers of a general linear projection pi: X --> P^{n+c}, with c > 0. When n is small it is classical that the degree of any fiber is bounded by n/c+1, but this fails for n >> 0. We describe a new invariant of the fiber that agrees with the degree in many cases and is always bounded by n/c+1. This implies, for example, that if we write a fiber as the disjoint union of schemes Y' and Y'' such that Y' is the union of the locally complete intersection components of Y, then deg Y'+deg Y''_red <= n/c+1 and this formula can be strengthened a little further. Our method also gives a sharp bound on the subvariety of P^r swept out by the l-secant lines of X for any positive integer l, and we discuss a corresponding bound for highly secant linear spaces of higher dimension. These results extend Ziv Ran's "Dimension+2 Secant Lemma".Comment: Proof of the main theorem simplified and new examples adde

Perceptions of Intellectual Property:A Review

In “The right to good ideas: patents and the poor”, The Economist depicts two driving forces in the contemporary discourse on IP and globalization. The one is interested in advancing the knowledge economy, an approach based on the belief that knowledge is the driving factor behind economic growth. The other resides on a belief that IP is a major means to advance the process of globalization. While the former is strongly motivated by new economic growth theory, as for example advanced by Stanford professor Paul Romer, the latter is based on typical anti-globalization arguments, such as for example the position that the IP system helps multinational companies to build up monopolies to the detriment of the poor, drives small and medium-sized enterprises (SMEs) and local business in developing countries out of business and increases prices for consumer products, be they pharmaceuticals or software. The purpose of this review is to help understand the current discourse on intellectual property, to grasp underlying themes, assumptions and connotations associated with the term “IP”, so as to identify paths leading to a more comprehensive understanding of IP and the opportunities and pitfalls it may provide

A single-merger scenario for the formation of the giant stream and the warp of M31

We propose that the accretion of a dwarf spheroidal galaxy provides a common origin for the giant southern stream and the warp of M31. We run about 40 full N-body simulations with live M31, infalling galaxies with varying masses and density profiles, and cosmologically-plausible initial orbital parameters. Excellent agreement with a full range of observational data is obtained for a model in which a dark-matter-rich dwarf spheroidal, whose trajectory lies on the thin plane of corotating satellites of M31, is accreted from its turnaround radius of about 200 kpcs into M31 at approximately 3 Gyrs ago. The satellite is disrupted as it orbits in the potential well of the galaxy and forms the giant stream and in return heats and warps the disk of M31. We show that our cosmologically-motivated model is favoured by the kinematic data over the phenomenological models in which the satellite starts its infall from a close distance of M31. Our model predicts that the remnant of the disrupted satellite resides in the region of the North-Eastern shelf of M31. The results here suggest that the surviving satellites of M31 that orbit on the same thin plane, as the disrupted satellite once did, could have all been accreted from an intergalactic filament.Comment: 18 pages, 22 figures, 3 table

Trademark owners perspective on the Madrid system: practical experiences and theoretical underpinnings

Based on the assumption that possible future reforms of the Madrid System for the filing and renewal of trademark registration at the international level must be user driven, the paper explored in a series of 23 in-depth interviews, the views of companies varying in size, geographical distribution, market context and number of trademarks filed for a company through the Madrid System. The empirical analysis underlined the important role of the Madrid System in expanding their market coverage, but also showed that a major challenge will be to meet the diverse needs of business operating in varied contexts of developing and developed countries. While firms in developed countries need a system that fits high-speed post-fordist business operations, further awareness raising and capacity building is necessary to fully integrate the private sector in developing countries and to expand participation beyond current usage levels.economic costs of trademark protection, user driven innovation, international trademark filing, international trade,