Stability conditions on curves

We study some examples of Bridgeland-Douglas stability conditions on triangulated categories. From one side we give a complete description of the stability manifolds for smooth projective curves of positive genus. From the other side we study stability conditions on triangulated categories generated by an exceptional collection. In the case of the projective line this leads to the connectedness and simply-connectedness of the stability manifold.Comment: 12 pages. Part of the preprint math/0411613. To appear in: Math. Res. Let

Fano varieties of cubic fourfolds containing a plane

We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other hand, we show that the Fano varieties are always birational to moduli spaces of twisted stable coherent sheaves on a K3 surface. The moduli spaces of complexes and of sheaves are related by wall-crossing in the derived category of twisted sheaves on the corresponding K3 surface.Comment: 26 pages. Many changes in the exposition. Final version to appear in Math. An

Projectivity and Birational Geometry of Bridgeland moduli spaces

We construct a family of nef divisor classes on every moduli space of stable complexes in the sense of Bridgeland. This divisor class varies naturally with the Bridgeland stability condition. For a generic stability condition on a K3 surface, we prove that this class is ample, thereby generalizing a result of Minamide, Yanagida, and Yoshioka. Our result also gives a systematic explanation of the relation between wall-crossing for Bridgeland-stability and the minimal model program for the moduli space. We give three applications of our method for classical moduli spaces of sheaves on a K3 surface: 1. We obtain a region in the ample cone in the moduli space of Gieseker-stable sheaves only depending on the lattice of the K3. 2. We determine the nef cone of the Hilbert scheme of n points on a K3 surface of Picard rank one when n is large compared to the genus. 3. We verify the "Hassett-Tschinkel/Huybrechts/Sawon" conjecture on the existence of a birational Lagrangian fibration for the Hilbert scheme in a new family of cases.Comment: v2: 50 pages, exposition substantially improved based on referee's comments. Accepted for publication in Journal of the AM

How Much Influence Do Economics Professors Have on Rankings? The Case of Australia and New Zealand

This study ranks Australian and New Zealand economics teaching departments on the basis of the research productivity of its economics professors in economics teaching departments using quality adjusted journal articles listed on the ECONLIT database for the periods 1988-2002 and for 1996-2002. The per capita research productivity of professors is highest for University of Melbourne, University of Western Australia and University of Canterbury. For a number of economics departments, the per capita research productivity is lower than the research productivity of all faculty members, using a number of criteria for 1988-2002 and 1996-2002. These universities are University of Auckland, Royal Melbourne Institute of Technology University, Griffith University and Macquarie University.research productivity; economics professors; rankings of economics departments

Financial development and economic growth: The case of eight Asian countries

This paper looks at the relationship between financial development and economic growth using time series data for eight Asian countries. First, we estimate augmented production functions where a financial development variable is added. Second, we conduct multivariate causality tests between the growth rate of income and the growth rates of the financial development variables. The regression results show a positive and significant relationship between the income variables and financial variables for India, Malaysia, Pakistan and Sri Lanka. The multivariate causality tests show a two-way causality relationship between the income and the financial variables for India and Malaysia, one-way causality from financial variables to income variables for Japan and Thailand and reverse causality for Korea, Pakistan and Philippines. Thus, our empirical results do not unambiguously support the general view of a clear and positive relationship between financial development and economic growth.finanacial development; economic growth; Asian countries

Inducing stability conditions

We study stability conditions induced by functors between triangulated categories. Given a finite group acting on a smooth projective variety we prove that the subset of invariant stability conditions embeds as a closed submanifold into the stability manifold of the equivariant derived category. As an application we examine stability conditions on Kummer and Enriques surfaces and we improve the derived version of the Torelli Theorem for the latter surfaces already present in the litterature. We also study the relationship between stability conditions on projective spaces and those on their canonical bundles.Comment: 31 pages. Final version to appear in J. Algebraic Geo

Cepheid Variables in the Maser-Host Galaxy NGC 4258

We present results of a ground-based survey for Cepheid variables in NGC 4258. This galaxy plays a key role in the Extragalactic Distance Scale due to its very precise and accurate distance determination via VLBI observations of water masers. We imaged two fields within this galaxy using the Gemini North telescope and GMOS, obtaining 16 epochs of data in the SDSS gri bands over 4 years. We carried out PSF photometry and detected 94 Cepheids with periods between 7 and 127 days, as well as an additional 215 variables which may be Cepheids or Population II pulsators. We used the Cepheid sample to test the absolute calibration of theoretical gri Period-Luminosity relations and found good agreement with the maser distance to this galaxy. The expected data products from the Large Synoptic Survey Telescope (LSST) should enable Cepheid searches out to at least 10 Mpc.Comment: Accepted for publication in the Astronomical Journa

Dipole Oscillations in Fermionic Mixtures

We study dipole oscillations in a general fermionic mixture: starting from the Boltzmann equation, we classify the different solutions in the parameter space through the number of real eigenvalues of the small oscillations matrix. We discuss how this number can be computed using the Sturm algorithm and its relation with the properties of the Laplace transform of the experimental quantities. After considering two components in harmonic potentials having different trapping frequencies, we study dipole oscillations in three-component mixtures. Explicit computations are done for realistic experimental setups using the classical Boltzmann equation without intra-species interactions. A brief discussion of the application of this classification to general collective oscillations is also presented.Comment: Published versio