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.

Magnetic field control of cycloidal domains and electric polarization in multiferroic BiFeO3_3

The magnetic field induced rearrangement of the cycloidal spin structure in ferroelectric mono-domain single crystals of the room-temperature multiferroic BiFeO$_3$ is studied using small-angle neutron scattering (SANS). The cycloid propagation vectors are observed to rotate when magnetic fields applied perpendicular to the rhombohedral (polar) axis exceed a pinning threshold value of $\sim$5\,T. In light of these experimental results, a phenomenological model is proposed that captures the rearrangement of the cycloidal domains, and we revisit the microscopic origin of the magnetoelectric effect. A new coupling between the magnetic anisotropy and the polarization is proposed that explains the recently discovered magnetoelectric polarization to the rhombohedral axis

Unfolded Description of AdS4AdS_4 Kerr Black Hole

It is shown that $AdS_4$ Kerr black hole is a solution of simple unfolded differential equations that form a deformation of the zero-curvature description of empty $AdS_4$ space-time. Our construction uses the Killing symmetries of the Kerr solution. All known and some new algebraic properties of the Kerr-Schild solution result from the obtained black hole unfolded system in the coordinate-independent way. Kerr Schild type solutions of free equations in $AdS_4$ for massless fields of any spin, associated to the proposed black hole unfolded system, are found.Comment: 18 page

Alpha-induced reactions for the astrophysical p-process: the case of 151Eu

The cross sections of 151Eu(alpha,gamma)155Tb and 151Eu(alpha,n)154Tb reactions have been measured with the activation method. Some aspects of the measurement are presented here to illustrate the requirements of experimental techniques needed to obtain nuclear data for the astrophysical p-process nucleosynthesis. Preliminary cross section results are also presented and compared with the predictions of statistical model calculations.Comment: Accepted for publication in Journal of Physics Conference Series, proceeding of the Nuclear Physics in Astrophysics IV. conferenc

Exploring context dependency in eco‐evolutionary patterns with the stick insect Timema cristinae

Rapid evolution can influence the ecology of populations, communities, and ecosystems, but the importance of evolution for ecological dynamics remains unclear, largely because the contexts in which evolution is powerful are poorly resolved. Here, we carry out a large observational study to test hypotheses about context dependency of eco‐evolutionary patterns previously identified on the stick insect Timema cristinae . Experiments and observations conducted in 2011 and 2012 documented predator‐mediated negative effects of camouflage maladaptation (i.e., evolutionary dynamics) on: (a) T. cristinae abundance and, (b) species richness and abundance of other arthropods. Here we show that camouflage maladaptation does not correlate with T. cristinae abundance and, instead, is associated with increased abundance and species richness of cohabitating arthropods. We furthermore find that plants with high levels of Timema maladaptation tend to have higher foliar nitrogen, that is, higher nutritional value, and more positive mass‐abundance slopes in the coexisting arthropod communities. We propose explanations for the observed contrasting results, such as negative density‐ and frequency‐dependent selection, feedbacks between herbivore abundance and plant nutritional quality, and common effects of predation pressure on selection and prey abundance. Our results demonstrate the utility of observational studies to assess the context dependency of eco‐evolutionary dynamics patterns and provide testable hypotheses for future work

Steady states in a structured epidemic model with Wentzell boundary condition

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we establish global existence of solutions and the Principle of Linearised Stability for our model. Then, in our main result, we formulate simple conditions, which guarantee the existence of non-trivial steady states of the model. Our method utilizes an operator theoretic framework combined with a fixed point approach. Finally, in the last section we establish a sufficient condition for the local asymptotic stability of the positive steady state

Remarks on the analytic structure of supersymmetric effective actions

We study the effective superpotential of N=1 supersymmetric gauge theories with a mass gap, whose analytic properties are encoded in an algebraic curve. We propose that the degree of the curve equals the number of semiclassical branches of the gauge theory. This is true for supersymmetric QCD with one adjoint and polynomial superpotential, where the two sheets of its hyperelliptic curve correspond to the gauge theory pseudoconfining and higgs branches. We verify this proposal in the new case of supersymmetric QCD with two adjoints and superpotential V(X)+XY^2, which is the confining phase deformation of the D_{n+2} SCFT. This theory has three kinds of classical vacua and its curve is cubic. Each of the three sheets of the curve corresponds to one of the three semiclassical branches of the gauge theory. We show that one can continuously interpolate between these branches by varying the couplings along the moduli space.Comment: 49 pages, 3 figures, harvmac; typos correcte

Precise half-life measurement of the 10 h isomer in 154Tb

The precise knowledge of the half-life of the reaction product is of crucial importance for a nuclear reaction cross section measurement carried out with the activation technique. The cross section of the 151Eu(alpha,n)154Tb reaction has been measured recently using the activation method, however, the half-life of the 10 h isomer in 154Tb has a relatively high uncertainty and ambiguous values can be found in the literature. Therefore, the precise half-life of the isomeric state has been measured and found to be 9.994 h +- 0.039 h. With careful analysis of the systematic errors, the uncertainty of this half-life value has been significantly reduced.Comment: Accepted for publication in Nuclear Physics