Singular del Pezzo fibrations and birational rigidity

A known conjecture of Grinenko in birational geometry asserts that a Mori fibre space with the structure of del Pezzo fibration of low degree is birationally rigid if and only if its anticanonical class is an interior point in the cone of mobile divisors. The conjecture is proved to be true for smooth models (with a generality assumption for degree 3). It is speculated that the conjecture holds for, at least, Gorenstein models in degree 1 and 2. In this article, I present a (Gorenstein) counterexample in degree 2 to this conjecture.Comment: This is essentially a more detailed version of the second section of arXiv:1310.5548. To appear in the proceedings of the conference 'Groups of Automorphisms in Birational and Affine Geometry', held in Trento, Italy, 201

Birational properties of pencils of del Pezzo surfaces of degree 1 and 2

We study the birational rigidity problem for smooth Mori fibrations on del Pezzo surfaces of degree 1 and 2. For degree 1 we obtain a complete description of rigid and non-rigid cases.Comment: AmsLatex, 22 page

Ramp wave loading experiments driven by heavy ion beams: a feasibility study

A new design for heavy-ion beam driven ramp wave loading experiments is suggested and analyzed. The proposed setup utilizes the long stopping ranges and the variable focal spot geometry of the high-energy uranium beams available at the GSI Helmholtzzentrum für Schwerionenforschung and Facility for Antiproton and Ion Research accelerator centers in Darmstadt, Germany. The release wave created by ion beams can be utilized to create a planar ramp loading of various samples. In such experiments, the predicted high pressure amplitudes (up to 10 Mbar) and short timescales of compression (<10 ns) will allow to test the time-dependent material deformation at unprecedented extreme conditions

Constraints on the total coupling strength to bosons in iron based superconductors

At present, there is still no consistent interpretation of the normal and superconducting properties of Fe-based superconductors (FeSCs). The strength of the el-el interaction and the role of correlation effects are under debate. Here, we examine several common materials and illustrate various problems and concepts that are generic for all FeSCs. Based on empirical observations and qualitative insight from density functional theory, we show that the superconducting and low-energy thermodynamic properties of the FeSCs can be described semi-quantitively within multiband Eliashberg theory. We account for an important high-energy mass renormalization phenomenologically,and in agreement with constraints provided by thermodynamic, optical, and angle-resolved photoemission data. When seen in this way, all FeSCs with $T_\mathrm{c} <$ 40~K studied so far are found to belong to an {\it intermediate} coupling regime. This finding is in contrast to the strong coupling scenarios proposed in the early period of the FeSC history.We also discuss several related issues, including the role of band shifts as measured by the positions of van Hove singularities, and the nature of a recently suggested quantum critical point in the strongly hole-doped systems AFe$_2$As$_2$ (A = K, Rb, Cs). Using high-precision full relativistic GGA-band structure calculations, we arrive at a somewhat milder mass renormalization in comparison with previous studies. From the calculated mass anisotropies of all Fermi surface sheets, only the $\varepsilon$-pocket near the corner of the BZ is compatible with the experimentally observed anisotropy of the upper critical field. pointing to its dominant role in the superconductivity of these three compounds.Comment: 19 pages, 9 figure