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.

Three embeddings of the Klein simple group into the Cremona group of rank three

We study the action of the Klein simple group G consisting of 168 elements on two rational threefolds: the three-dimensional projective space and a smooth Fano threefold X of anticanonical degree 22 and index 1. We show that the Cremona group of rank three has at least three non-conjugate subgroups isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein metric, and we construct a smooth polarized K3 surface of degree 22 with an action of the group G.Comment: 43 page

Geometric invariant theory of syzygies, with applications to moduli spaces

We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium 2017, v2: final version, corrects a sign error and resulting divisor class calculations on the moduli space of K3 surfaces in Section 5, other minor changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha

Evaluating inputs for organic farming – a new system. Proposals of the ORGANIC INPUTS EVALUATION project

This volume contains proposals for criteria for evaluation of plant protection products, fertilisers and soil conditioners1 to be used in organic agriculture. These ideas were developed in the course of the European Union (EU) Concerted Action project ‘ORGANIC INPUTS EVALUATION’ (QLK5-CT-2002-02565). For more information on this project see the end of this volume or visit the project website www.organicinputs.org. The documents in this volume are proposals elaborated by the project consortium and external experts. They were discussed with a broader audience at a public conference held in Brussels on October 13, 2005, and have been amended accordingly. Our proposals also include a “criteria matrix”, which is in Microsoft Excel format, and therefore stands as a separate file. The criteria matrix is discussed in section 5, but we strongly recommend that you consult the original document. To illustrate the use of the matrix, we have further prepared two case studies, which are also separate Excel files. All of these files are contained on the CD, and can also be downloaded from the project website. Currently, Regulation 2092/91 is under revision. We hope that our ideas can be incorporated into the regulation during this revision! In addition, we strongly encourage national institutions to make use of our proposals at the national level

A 13CO and C18O Survey of the Molecular Gas Around Young Stellar Clusters Within 1kpc of the Sun

As the first step of a multi-wavelength investigation into the relationship between young stellar clusters and their environment we present fully-sampled maps in the J=1--0 lines of 13CO and C18O and the J=2--1 line of C18O for a selected group of thirty young stellar groups and clusters within 1kpc of the Sun. This is the first systematic survey of these regions to date. The clusters range in size from several stars to a few hundred stars. Thirty fields ranging in size from 8'x 8' to 60'x 30' were mapped with 47'' resolution simultaneously in the J=1-0 lines with Five College Radio Observatory. Seventeen sources were mapped over fields ranging in size from 3'x 3' to 13'x 13' in the J=2--1 line with 35'' resolution with the Heinrich Hertz Telescope. We compare the cloud properties derived from each of the three tracers in order to better understand systematic uncertainties in determing masses and linewidths. Cloud masses are determined independently using the 13CO and C18O transitions, these masses range from 30 to 4000 M_sun. Finally, we present a simple morphological classification scheme which may serve as a rough indicator of cloud evolution.Comment: 52 pages, 29 figures. Accepted for publication in AJ. Some figures have been reduced in resolution, a full resolution version is available from http://daisy.astro.umass.edu/~naomi/pubs/pubs.htm

Measurements of fiducial and differential cross sections for Higgs boson production in the diphoton decay channel at s√=8 TeV with ATLAS

Measurements of fiducial and differential cross sections are presented for Higgs boson production in proton-proton collisions at a centre-of-mass energy of s√=8 TeV. The analysis is performed in the H → γγ decay channel using 20.3 fb−1 of data recorded by the ATLAS experiment at the CERN Large Hadron Collider. The signal is extracted using a fit to the diphoton invariant mass spectrum assuming that the width of the resonance is much smaller than the experimental resolution. The signal yields are corrected for the effects of detector inefficiency and resolution. The pp → H → γγ fiducial cross section is measured to be 43.2 ±9.4(stat.) − 2.9 + 3.2 (syst.) ±1.2(lumi)fb for a Higgs boson of mass 125.4GeV decaying to two isolated photons that have transverse momentum greater than 35% and 25% of the diphoton invariant mass and each with absolute pseudorapidity less than 2.37. Four additional fiducial cross sections and two cross-section limits are presented in phase space regions that test the theoretical modelling of different Higgs boson production mechanisms, or are sensitive to physics beyond the Standard Model. Differential cross sections are also presented, as a function of variables related to the diphoton kinematics and the jet activity produced in the Higgs boson events. The observed spectra are statistically limited but broadly in line with the theoretical expectations

Circumstellar disks and planets. Science cases for next-generation optical/infrared long-baseline interferometers

We present a review of the interplay between the evolution of circumstellar disks and the formation of planets, both from the perspective of theoretical models and dedicated observations. Based on this, we identify and discuss fundamental questions concerning the formation and evolution of circumstellar disks and planets which can be addressed in the near future with optical and infrared long-baseline interferometers. Furthermore, the importance of complementary observations with long-baseline (sub)millimeter interferometers and high-sensitivity infrared observatories is outlined.Comment: 83 pages; Accepted for publication in "Astronomy and Astrophysics Review"; The final publication is available at http://www.springerlink.co

Search for squarks and gluinos in events with isolated leptons, jets and missing transverse momentum at s√=8 TeV with the ATLAS detector

The results of a search for supersymmetry in final states containing at least one isolated lepton (electron or muon), jets and large missing transverse momentum with the ATLAS detector at the Large Hadron Collider are reported. The search is based on proton-proton collision data at a centre-of-mass energy s√=8 TeV collected in 2012, corresponding to an integrated luminosity of 20 fb−1. No significant excess above the Standard Model expectation is observed. Limits are set on supersymmetric particle masses for various supersymmetric models. Depending on the model, the search excludes gluino masses up to 1.32 TeV and squark masses up to 840 GeV. Limits are also set on the parameters of a minimal universal extra dimension model, excluding a compactification radius of 1/R c = 950 GeV for a cut-off scale times radius (ΛR c) of approximately 30

Evidence for the Higgs-boson Yukawa coupling to tau leptons with the ATLAS detector

Results of a search for H → τ τ decays are presented, based on the full set of proton-proton collision data recorded by the ATLAS experiment at the LHC during 2011 and 2012. The data correspond to integrated luminosities of 4.5 fb−1 and 20.3 fb−1 at centre-of-mass energies of √s = 7 TeV and √s = 8 TeV respectively. All combinations of leptonic (τ → `νν¯ with ` = e, µ) and hadronic (τ → hadrons ν) tau decays are considered. An excess of events over the expected background from other Standard Model processes is found with an observed (expected) significance of 4.5 (3.4) standard deviations. This excess provides evidence for the direct coupling of the recently discovered Higgs boson to fermions. The measured signal strength, normalised to the Standard Model expectation, of µ = 1.43 +0.43 −0.37 is consistent with the predicted Yukawa coupling strength in the Standard Model