Performance of a Highly Granular Scintillator-SiPM Based Hadron Calorimeter Prototype in Strong Magnetic Fields

Within the CALICE collaboration, several concepts for the hadronic calorimeter of a future linear collider detector are studied. After having demonstrated the capabilities of the measurement methods in "physics prototypes", the focus now lies on improving their implementation in "engineering prototypes", that are scalable to the full linear collider detector. The Analog Hadron Calorimeter (AHCAL) concept is a sampling calorimeter of tungsten or steel absorber plates and plastic scintillator tiles read out by silicon photomultipliers (SiPMs) as active material. The front-end chips are integrated into the active layers of the calorimeter and are designed for minimizing power consumption by rapidly cycling the power according to the beam structure of a linear accelerator. The versatile electronics allows the prototype to be equipped with different types of scintillator tiles and SiPMs. A prototype with ~2200 channels, equipped with several types of scintillator tiles and SiPMs, was tested with muons and electrons in a 1.5 T magnet at the CERN SPS in May 2017 to establish the operational stability with power pulsing and the overall detector performance in a magnetic field.Comment: 4 pages, 9 figures, IEEE NSS/MIC 2017 Conference Recor

On stable rationality of some conic bundles and moduli spaces of Prym curves

We prove that a very general hypersurface of bidegree (2, n) in P^2 x P^2 for n bigger than or equal to 2 is not stably rational, using Voisin's method of integral Chow-theoretic decompositions of the diagonal and their preservation under mild degenerations. At the same time, we also analyse possible ways to degenerate Prym curves, and the way how various loci inside the moduli space of stable Prym curves are nested. No deformation theory of stacks or sheaves of Azumaya algebras like in recent work of Hasset-Kresch-Tschinkel is used, rather we employ a more elementary and explicit approach via Koszul complexes, which is enough to treat this special case.Comment: 23 pages; Macaulay 2 code used for verification of parts of the paper available at http://www.math.uni-hamburg.de/home/bothmer/m2.html and at the end of the TeX file; v2: in section 4, we now included a proof of the main theorem that works for all n (unconditional on the parity) that was communicated to us by Zhi Jiang, Zhiyu Tian, and Letao Zhang. Several other minor expository improvement

Degenerations of Gushel-Mukai fourfolds, with a view towards irrationality proofs

We study a certain class of degenerations of Gushel-Mukai fourfolds as conic bundles, which we call tame degenerations and which are natural if one wants to prove that very general Gushel-Mukai fourfolds are irrational using the degeneration method due to Voisin, Colliot-Th\'{e}l\`{e}ne-Pirutka, Totaro et al. However, we prove that no such tame degenerations do exist.Comment: 25 page

Experimental results for the Poincar\'e center problem (including an Appendix with Martin Cremer)

We apply a heuristic method based on counting points over finite fields to the Poincar\'e center problem. We show that this method gives the correct results for homogeneous non linearities of degree 2 and 3. Also we obtain new evidence for Zoladek's conjecture about general degree 3 non linearitiesComment: 16 pages, 2 figures, source code of programs at http://www-ifm.math.uni-hannover.de/~bothmer/strudel/. Added references, the result of Example 6.2 is not new. Added two new sections on rationally reversible systems. The 4th codim 7 component we saw only experimentally can now also be identified geometrical

Significance of log-periodic signatures in cumulative noise

Using methods introduced by Scargle in 1978 we derive a cumulative version of the Lomb periodogram that exhibits frequency independent statistics when applied to cumulative noise. We show how this cumulative Lomb periodogram allows us to estimate the significance of log-periodic signatures in the S&P 500 anti-bubble that started in August 2000.Comment: 14 pages, 7 figures; AMS-Latex; introduction rewritten, some points of the exposition clarified. Author-supplied PDF file with high resolution graphics is available at http://btm8x5.mat.uni-bayreuth.de/~bothmer

Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface

Based on a recent result of Voisin [2001] we describe the last nonzero syzygy space in the linear strand of a canonical curve C of even genus g=2k lying on a K3 surface, as the ambient space of a k-2-uple embedded P^{k+1}. Furthermore the geometric syzygies constructed by Green and Lazarsfeld [1984] from g^1_{k+1}'s form a non degenerate configuration of finitely many rational normal curves on this P^{k+1}. This proves a natural generalization of Green's conjecture [1984], namely that the geometric syzygies should span the space of all syzygies, in this case.Comment: 29 pages; 5 figure

The transcendental lattice of the sextic Fermat surface

We prove that the integral polarized Hodge structure on the transcendental lattice of a sextic Fermat surface is decomposable. This disproves a conjecture of Kulikov related to a Hodge theoretic approach to proving the irrationality of the very general cubic fourfold.Comment: 15 pages; v2: minor changes, streamlined the argument in Section