Quasihomogeneity of curves and the Jacobian endomorphism ring

We give a quasihomogeneity criterion for Gorenstein curves. For complete intersections, it is related to the first step of Vasconcelos' normalization algorithm. In the process, we give a simplified proof of the Kunz-Ruppert criterion.Comment: 9 page

Derivations of negative degree on quasihomogeneous isolated complete intersection singularities

J. Wahl conjectured that every quasihomogeneous isolated normal singularity admits a positive grading for which there are no derivations of negative weighted degree. We confirm his conjecture for quasihomogeneous isolated complete intersection singularities of either order at least 3 or embedding dimension at most 5. For each embedding dimension larger than 5 (and each dimension larger than 3), we give a counter-example to Wahl's conjecture.Comment: 11 page

On the formal structure of logarithmic vector fields

In this article, we prove that a free divisor in a three dimensional complex manifold must be Euler homogeneous in a strong sense if the cohomology of its complement is the hypercohomology of its logarithmic differential forms. F.J. Calderon-Moreno et al. conjectured this implication in all dimensions and proved it in dimension two. We prove a theorem which describes in all dimensions a special minimal system of generators for the module of formal logarithmic vector fields. This formal structure theorem is closely related to the formal decomposition of a vector field by Kyoji Saito and is used in the proof of the above result. Another consequence of the formal structure theorem is that the truncated Lie algebras of logarithmic vector fields up to dimension three are solvable. We give an example that this may fail in higher dimensions.Comment: 13 page

MicroPoem: experimental investigation of birch pollen emissions

Diseases due to aeroallergens constantly increased over the last decades and affect more and more people. Adequate protective and pre-emptive measures require both reliable assessment of production and release of various pollen species, and the forecasting of their atmospheric dispersion. Pollen forecast models, which may be either based on statistical knowledge or full physical transport and dispersion modeling, can provide pollen forecasts with full spatial coverage. Such models are currently being developed in many countries. The most important shortcoming in these pollen transport systems is the description of emissions, namely the dependence of the emission rate on physical processes such as turbulent exchange or mean transport and biological processes such as ripening (temperature) and preparedness for release. Thus the quantification of pollen emissions and determination of the governing mesoscale and micrometeorological factors are subject of the present project MicroPoem, which includes experimental field work as well as numerical modeling. The overall goal of the project is to derive an emission parameterization based on meteorological parameters, eventually leading to enhanced pollen forecasts. In order to have a well-defined source location, an isolated birch pollen stand was chosen for the set-up of a ‘natural tracer experiment', which was conducted during the birch pollen season in spring 2009. The site was located in a broad valley, where a mountain-plains wind system usually became effective during clear weather periods. This condition allowed to presume a rather persistent wind direction and considerable velocity during day- and nighttime. Several micrometeorological towers were operated up- and downwind of this reference source and an array of 26 pollen traps was laid out to observe the spatio-temporal variability of pollen concentrations. Additionally, the lower boundary layer was probed by means of a sodar and a tethered balloon system (also yielding a pollen concentration profile). In the present contribution a project overview is given and first results are presented. An emphasis is put on the relative performance of different sample technologies and the corresponding relative calibration in the lab and the field. The concentration distribution downwind of the birch stand exhibits a significant spatial (and temporal) variability. Small-scale numerical dispersion modeling will be used to infer the emission characteristics that optimally explain the observed concentration patterns

Partial normalizations of coxeter arrangements and discriminants

We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovin’s Frobenius manifold structure which is lifted (without unit) to the space of the arrangement. We also describe an independent approach to these structures via duality of maximal Cohen–Macaulay fractional ideals. In the process, we find 3rd order differential relations for the basic invariants of the Coxeter group. Finally, we show that our partial normalizations give rise to new free divisors

Fourier's Law confirmed for a class of small quantum systems

Within the Lindblad formalism we consider an interacting spin chain coupled locally to heat baths. We investigate the dependence of the energy transport on the type of interaction in the system as well as on the overall interaction strength. For a large class of couplings we find a normal heat conduction and confirm Fourier's Law. In a fully quantum mechanical approach linear transport behavior appears to be generic even for small quantum systems.Comment: 6 pages, 8 figure