Kahler-Einstein metrics on symmetric Fano T-varieties

We relate the global log canonical threshold of a variety with torus action to the global log canonical threshold of its quotient. We apply this to certain Fano varieties and use Tian's criterion to prove the existence of Kahler-Einstein metrics on them. In particular, we obtain simple examples of Fano threefolds being Kahler-Einstein but admitting deformations without Kahler-Einstein metric.Comment: 12 pages, main theorem slightly improved + minor correction

Normal singularities with torus actions

We propose a method to compute a desingularization of a normal affine variety X endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the structure of the singularities of X. In particular, we give criteria for X to have only rational, (QQ-)factorial, or (QQ-)Gorenstein singularities. We also give partial criteria for X to be Cohen-Macaulay or log-terminal. Finally, we provide a method to construct factorial affine varieties with a torus action. This leads to a full classification of such varieties in the case where the action is of complexity one.Comment: 23 page

On the Cox ring of blowing up the diagonal

We compute the Cox rings of the blow-ups $\mathrm{Bl}_\Delta(X'\times X')$ and $\mathrm{Bl}_\Delta(\mathbb P_1^n)$ where $X'$ is a product of projective spaces and $\Delta$ is the (generalised) diagonal.Comment: 8 page

Resolution studies with the DATURA beam telescope

Detailed studies of the resolution of a EUDET-type beam telescope are carried out using the DATURA beam telescope as an example. The EUDET-type beam telescopes make use of CMOS MIMOSA 26 pixel detectors for particle tracking allowing for precise characterisation of particle sensing devices. A profound understanding of the performance of the beam telescope as a whole is obtained by a detailed characterisation of the sensors themselves. The differential intrinsic resolution as measured in a MIMOSA 26 sensor is extracted using an iterative pull method and various quantities that depend on the size of the cluster are discussed: the residual distribution, the intra-pixel residual-width distribution and the intra-pixel density distribution of track incident positions

Shanks-transform accelerated PML-based series expansions for the 1-D periodic 3-D Green's functions of multilayered media

A PerfectlyMatched Layer (PML) based formalismis proposed to derive fast converging series expansions for the 1D periodic 3D Green’s functions of layered media. The Shanks transform is applied to accelerate the PML-based series