Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

The upgrade of the ALICE TPC with GEMs and continuous readout

The upgrade of the ALICE TPC will allow the experiment to cope with the high interaction rates foreseen for the forthcoming Run 3 and Run 4 at the CERN LHC. In this article, we describe the design of new readout chambers and front-end electronics, which are driven by the goals of the experiment. Gas Electron Multiplier (GEM) detectors arranged in stacks containing four GEMs each, and continuous readout electronics based on the SAMPA chip, an ALICE development, are replacing the previous elements. The construction of these new elements, together with their associated quality control procedures, is explained in detail. Finally, the readout chamber and front-end electronics cards replacement, together with the commissioning of the detector prior to installation in the experimental cavern, are presented. After a nine-year period of R&D, construction, and assembly, the upgrade of the TPC was completed in 2020.publishedVersio

The ALICE experiment at the CERN LHC

ALICE (A Large Ion Collider Experiment) is a general-purpose, heavy-ion detector at the CERN LHC which focuses on QCD, the strong-interaction sector of the Standard Model. It is designed to address the physics of strongly interacting matter and the quark-gluon plasma at extreme values of energy density and temperature in nucleus-nucleus collisions. Besides running with Pb ions, the physics programme includes collisions with lighter ions, lower energy running and dedicated proton-nucleus runs. ALICE will also take data with proton beams at the top LHC energy to collect reference data for the heavy-ion programme and to address several QCD topics for which ALICE is complementary to the other LHC detectors. The ALICE detector has been built by a collaboration including currently over 1000 physicists and engineers from 105 Institutes in 30 countries. Its overall dimensions are 161626 m3 with a total weight of approximately 10 000 t. The experiment consists of 18 different detector systems each with its own specific technology choice and design constraints, driven both by the physics requirements and the experimental conditions expected at LHC. The most stringent design constraint is to cope with the extreme particle multiplicity anticipated in central Pb-Pb collisions. The different subsystems were optimized to provide high-momentum resolution as well as excellent Particle Identification (PID) over a broad range in momentum, up to the highest multiplicities predicted for LHC. This will allow for comprehensive studies of hadrons, electrons, muons, and photons produced in the collision of heavy nuclei. Most detector systems are scheduled to be installed and ready for data taking by mid-2008 when the LHC is scheduled to start operation, with the exception of parts of the Photon Spectrometer (PHOS), Transition Radiation Detector (TRD) and Electro Magnetic Calorimeter (EMCal). These detectors will be completed for the high-luminosity ion run expected in 2010. This paper describes in detail the detector components as installed for the first data taking in the summer of 2008