Het geheim van het recht

Rectorale oratie Vrije Universiteit 196

Moduli spaces and algebraic cycles in real algebraic geometry

This thesis intends to make a contribution to the theories of algebraic cycles and moduli spaces over the real numbers. In the study of the subvarieties of a projective algebraic variety, smooth over the field of real numbers, the cycle class map between the Chow ring and the equivariant cohomology ring plays an important role. The image of the cycle class map remains difficult to describe in general; we study this group in detail in the case of real abelian varieties. To do so, we construct integral Fourier transforms on Chow rings of abelian varieties over any field. They allow us to prove the integral Hodge conjecture for one-cycles on complex Jacobian varieties, and the real integral Hodge conjecture modulo torsion for real abelian threefolds. For the theory of real algebraic cycles, and for several other purposes in real algebraic geometry, it is useful to have moduli spaces of real varieties to our disposal. Insight in the topology of a real moduli space provides insight in the geometry of a real variety that defines a point in it, and the other way around. In the moduli space of real abelian varieties, as well as in the Torelli locus contained in it, we prove density of the set of moduli points attached to abelian varieties containing an abelian subvariety of fixed dimension. Moreover, we provide the moduli space of stable real binary quintics with a hyperbolic orbifold structure, compatible with the period map on the locus of smooth quintics. This identifies the moduli space of stable real binary quintics with a non-arithmetic ball quotient.Comment: 234 pages, PhD thesi

Non-arithmetic uniformization of metric spaces attached to unitary Shimura varieties

We develop a new method of constructing non-arithmetic lattices in the projective orthogonal group $\text{PO}(n,1)$ for every integer $n$ larger than one. The technique is to consider anti-holomorphic involutions on a complex arithmetic ball quotient, glue their fixed loci along geodesic subspaces, and show that the resulting metric space carries canonically the structure of a complete real hyperbolic orbifold. The volume of various of these non-arithmetic orbifolds can be explicitly calculated.Comment: 39 pages. v3: remarks added in Section 1.2, concerning a comparison with the Gromov--Piatetski-Shapiro construction, and the volume of the constructed hyperbolic orbifold

On the integral Hodge conjecture for real abelian threefolds

We prove the real integral Hodge conjecture for several classes of real abelian threefolds. For instance, we prove the property for real abelian threefolds $A$ whose real locus $A(\mathbb R)$ is connected, and for real abelian threefolds $A$ which are a product $A = B \times E$ of an abelian surface $B$ and an elliptic curve $E$ with connected real locus $E(\mathbb R)$. Moreover, we show that every real abelian threefold satisfies the real integral Hodge conjecture modulo torsion, and reduce the general case to the Jacobian case.Comment: 32 pages. arXiv admin note: substantial text overlap with arXiv:2211.0271

From dissociated hegemony towards embedded hegemony: Multilateralism as a by-product of American security concerns

An earlier paper by the second author, entitled ‘Bella Americana: Some Consequences for the International Community’, dealt with the background and consequences of the American dissociation from the international legal and political order created after World War II. The current article examines this divergence in the light of United States foreign policy in general, pointing out that hegemony, unilateralism and pre-emptive strike together represent a certain ‘constant’ in American foreign policy. The article then examines the so called ‘war on terror’, trying to understand its flaws within the context of American strategic culture. Arguably, however, what has changed after 9/11 is not just the nature of security threats as such but also the global environment in which these manifest themselves. Taking supremacy of the world’s military, technological and financial-economic superpower as a basis for further analysis, the issue becomes how to get that hegemony embedded in a multilateral setting. Here the notion of ‘policy by-products’ appears to open new venues. Continuing unilateralism, the article argues, would constitute a serious threat to American security proper

Violence among peoples in the light of human frustration and aggression

This article sets out to provide a general background to the study of aggression in the social sciences, with a particular focus on its link to collective violence. While the study of what happens in the human brain appears to be already highly complex, analysis of violent behavior appears to be even more intricate. A deductive system in the sense of a general and clear system of propositions logically connected to one another is not feasible, principally because contrary to the natural sciences there are no verities but merely “stylized facts.” One of these concerns the setting of human aggression in the light of frustration, as argued in the frustration–aggression hypothesis developed by Dollard et al. in 1939. Apart from conceiving of aggression as a pure human instinct, it may also be seen as externally driven, while a third possibility concerns culturally “learned” aggression. Proof of the latter is that the strongest correlation appears to be that between current violence and previous manifestations thereof. Attention is paid to the way in which Gurr has rooted his relative deprivation theory on causes of collective violence among peoples in mechanisms of frustration and aggression. That theory is taken a bit further in terms of “perceived acquirement failure,” which appears to be highly connected to the role of the state. Based on certain observations by Hannah Arendt, the argument then proceeds to violence as a manifestation of powerlessness. Finally, this leads to a discussion of justice as a crucial factor in what Durkheim used to call a “right to conflict.” In this way, human aggression is placed in a broad socio-economic context

The human rights mission in an African context

In the annual sessions of the United Nations Commission on Human Rights in Geneva, resolutions condemning African governments for gross and systematic violations of human rights are usually rejected with the whole African block against. Through such block voting even President Mugabe’s policies and actions against the rule of law in Zimbabwe have remained uncensored. Indeed, Africa’s record in the international venture for the realization of human rights looks rather dim. Whereas international human rights do not in any way refer to spiritual roots of the conviction that human dignity must be protected against any abuse of power, in an African setting it is abundantly clear that human rights is a mission that cannot be separated from people’s religious convictions and commitment. In Chichewa the word for God is Mulungu while justice is Chi-lung-amo. God, in other words, is the Upright one, while justice is to do God’s will. That connection is not an invention of the missionaries. It manifests the spiritual strength in which human rights in Africa might build upon a conviction rooted in African culture through the ages

Is socialism possible?

Apparently transition is a difficult process. The reform programme adopted in Russia and several other former socialist countries was based on a purely economic approach, neglecting socio-cultural and political conditions for successful transition. These conditions are still largely determined by the socialist project that preceded the current transition process. Hence any study of transition has to start exploring the question: Transition from what? What, exactly, is wrong with socialism

Good governance in an African perspective: an essay on actors and actions

In preparation for this conference I have looked back at my own work and the work of others in the period just after most of Sub-Saharan Africa achieved independence. My own place was in the University of Zambia, from 1967 to 1971. Perusing our publications of the late sixties and early seventies of this quickly passing century, what strikes me is first of all our belief in the new politics as a basis for development. Not without reason colonialism had been regarded as the basic constraint to improvement of people's living conditions and to political integration. In most African countries those fighting for freedom had overcome. The independent African state not merely signified political liberty, it would also constitute the primary instrument towards the uplifting of its own people. A remaining constraint was of course white minority power in much of Southern Africa but liberation was certain. "One day", my colleague Richard Sklar exclaimed, "African nations will negotiate from strength.