Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

Selection in Scale-Free Small World

In this paper we compare the performance characteristics of our selection based learning algorithm for Web crawlers with the characteristics of the reinforcement learning algorithm. The task of the crawlers is to find new information on the Web. The selection algorithm, called weblog update, modifies the starting URL lists of our crawlers based on the found URLs containing new information. The reinforcement learning algorithm modifies the URL orderings of the crawlers based on the received reinforcements for submitted documents. We performed simulations based on data collected from the Web. The collected portion of the Web is typical and exhibits scale-free small world (SFSW) structure. We have found that on this SFSW, the weblog update algorithm performs better than the reinforcement learning algorithm. It finds the new information faster than the reinforcement learning algorithm and has better new information/all submitted documents ratio. We believe that the advantages of the selection algorithm over reinforcement learning algorithm is due to the small world property of the Web.Comment: 24 pages, 3 figure

Gravity from the extension of spatial diffeomorphisms

The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential term which can be a general (not necessarily local) functional of the metric. From the perspective of the foundation of Einstein's gravity our results are positive: The extended constraint algebra is either that of Einstein's gravity, or ultralocal gravity. If our goal is a simple modification of Einstein's gravity that for example makes it perturbatively renormalizable, as has recently been suggested, then our results show that there is no such theory within this class.Comment: 34 page

Production Technology and Competitiveness In the Hungarian Manufacturing Industry

Following the big transformations of the 1990s, enterprise structure and technological level seem to have become stabilised in Hungary. Under these circumstances it is especially interesting to identify the elements responsible for competitiveness in general, and the role technology plays in development in particular, according to managers experienced in production and marketing. This empirical study – based on in-depth interviews and field research – summarises characteristics of the technological level in the sectors examined, role of technology and labour in production, effects of foreign direct investment, relations between competition and firm-level factors determining competitiveness, and concludes by summing up those most frequently mentioned proposals that should be incorporated into economic policy according to managers. Main findings indicate that more qualified, more intensive and cheaper labour can be substituted for high technology. The competitiveness of an enterprise is not determined by technology alone, but rather by a combination of technology, the parameters of available labour and the costs of investment increasing productivity. The insufficiency of inter-company relations, together with a shortage of available assets necessary for investment constitute the major threat undermining the competitiveness of enterprises in present-day Hungary

An extremal effective survey about extremal effective cycles in moduli spaces of curves

We survey recent developments and open problems about extremal effective divisors and higher codimension cycles in moduli spaces of curves.Comment: Submitted to the Proceedings of the Abel Symposium 2017. Comments are welcom