Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds

We prove that the moduli spaces A_3(D) of polarized abelian threefolds with polarizations of types D=(1,1,2), (1,2,2), (1,1,3) or (1,3,3) are unirational. The result is based on the study of families of simple coverings of elliptic curves of degree 2 or 3 and on the study of the corresponding period mappings associated with holomorphic differentials with trace 0. In particular we prove the unirationality of the Hurwitz space H_{3,A}(Y) which parameterizes simply branched triple coverings of an elliptic curve Y with determinants of the Tschirnhausen modules isomorphic to A^{-1}.Comment: 43 pages, latex2e, some typos corrected, references updated, to appear in Annali di Matematica Pura ed Applicat

Possible Worlds in the Precipice: Why Leibniz Met Spinoza?

The main objective of the paper is to give initial answers to three important questions. Why did Leibniz visit Spinoza? Why did his preparation for this meeting include a modification of the ontological proof of God? What is the philosophical result of the meeting and what do possible worlds have to do with it? In order to provide answers, three closely related manuscripts by Leibniz from November 1676 have been compared and the slow conceptual change of his philosophical apparatus has been analyzed. The last of these manuscripts was presented and read in front of Spinoza. Around that time Leibniz abandoned the idea of plurality of worlds (cf. Tschirnhaus) and instead proposed the idea of possible worlds, thus introducing possibility into the (onto/theo)logical structure itself in order to avoid the “precipice” of Spinoza’s necessity. What is interesting, however, is how exactly this conceptual change occurred at the end of 1676 and what its philosophical and methodological implications are

Irreducibility of Hurwitz spaces

Graber, Harris and Starr proved, when n >= 2d, the irreducibility of the Hurwitz space H^0_{d,n}(Y) which parametrizes degree d coverings of a smooth, projective curve Y of positive genus, simply branched in n points, with full monodromy group S_d (math.AG/0205056). We sharpen this result and prove that H^0_{d,n}(Y) is irreducible if n >= max{2,2d-4} and in the case of elliptic Y if n >= max{2,2d-6}. We extend the result to coverings simply branched in all but one point of the discriminant. Fixing the ramification multiplicities over the special point we prove that the corresponding Hurwitz space is irreducible if the number of simply branched points is >= 2d-2. We study also simply branched coverings with monodromy group different from S_d and when n is large enough determine the corresponding connected components of H_{d,n}(Y). Our results are based on explicit calculation of the braid moves associated with the standard generators of the n-strand braid group of Y.Comment: latex2e, 34 pages, 5 figure

New Wars on the Balkans - Business as Usual

The monopoly over the exercise of violence is the main defining element of states according to the Weberian ideal-type taxonomy. (Weber 1991, in Jung, 78) However, the ability to wield effective control over a fixed territory and to use physical force, extract taxes and operate a system of arbitration has been claimed and successfully attained by other actors. The military conflict in Former Yugoslavia, which raged throughout the 1990s and has serious implications to this day, has often been assessed in humanitarian and traditional International Relations terms. In this paper, I discuss the Balkan conflicts as 'New Wars' which unlike traditional statist military exercise pose a lot more questions and confront one's perceptions of right and wrong.New Wars; Balkans; violence; smuggling; conflict

Economic Development in the Maghreb States in the Context of their Relations with the EU

This paper examines a number of key factors that have an impact on economic development in the Maghreb. While growth indicators have been favorable in recent years, a consideration of the inequitable distribution of wealth and the precarious employment situation paint a different picture. Furthermore, the Maghreb economies have remained over-regulated and plagued by a host of structural constraints, prominent among which is the excessive role of the state. The record of the Euro-Mediterranean partnership has also been mixed. Critics have stated that it is compromised by turf battles within the EU, which render it incapable of providing the right solutions for the Maghreb states’ problems. The paper argues that a failure to tackle agriculture as an issue of prime importance for poverty reduction may exacerbate present inequalities and social imbalances in the Maghreb.EU; ENP; Euromed; trade; Maghreb; North Africa; Mediterranean; development