Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)

We prove that the moduli space A_3(1,1,4) of polarized abelian threefolds with polarization of type (1,1,4) is unirational. By a result of Birkenhake and Lange this implies the unirationality of the isomorphic moduli space A_3(1,4,4). The result is based on the study the Hurwitz space H_{4,n}(Y) of quadruple coverings of an elliptic curve Y simply branched in n points. We prove the unirationality of its codimension one subvariety H^{0}_{4,A}(Y) which parametrizes quadruple coverings \pi:X --> Y with Tschirnhausen modules isomorphic to A^{-1}, where A\in Pic^{n/2}Y, and for which \pi^*:J(Y)--> J(X) is injective. This is an analog of the result of Arbarello and Cornalba that the Hurwitz space H_{4,n}(P^1) is unirational.Comment: 28 pages, amslatex, to appear in Mathematische Nachrichte

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.

Prerequisites for setting up management system in municipal retail trade

The relevance of the problem is determined by the number of complex problems that exist in present Samara municipal retail trade system, which is manifested in the lack of regulation, a glut of sales area, poorly developed infrastructure. The purpose of this article is to form a quantitative base for determining the municipal needs in the floor space. Leading method to study this problem is the method of empirical observations and mathematical modeling. The study results: the article contains the analysis of sales area availability on the example in the urban district and presents a quantitative method to determine predictive values for retail trade turnover. Practical significance: the paper is aimed to develop managerial decisions in the sphere of municipal trade regulation. © 2016 Suraeva et al

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

The new small-angle neutron scattering instrument SANS-1 at MLZ—characterization and first results

AbstractA thorough characterization of the key features of the new small-angle neutron scattering instrument SANS-1 at MLZ, a joint project of Technische Universität München and Helmholtz Zentrum Geesthacht, is presented. Measurements of the neutron beam profile, divergency and flux are given for various positions along the instrument including the sample position, and agree well with Monte Carlo simulations of SANS-1 using the program McStas. Secondly, the polarization option of SANS-1 is characterized for a broad wavelength band. A key feature of SANS-1 is the large accessible Q-range facilitated by the sideways movement of the detector. Particular attention is hence paid to the effects that arise due to large scattering angles on the detector where a standard cos3 solid angle correction is no longer applicable. Finally the performance of the instrument is characterized by a set of standard samples

Phase Diagram of Multilayer Magnetic Structures

Multilayer "ferromagnet-layered antiferromagnet" (Fe/Cr) structures frustrated due to the roughness of layer interfaces are studied by numerical modeling methods. The "thickness-roughness" phase diagrams for the case of thin ferromagnetic film on the surface of bulk antiferromagnet and for two ferromagnetic layers separated by an antiferromagnetic interlayer are obtained and the order parameter distributions for all phases are found. The phase transitions nature in such systems is considered. The range of applicability for the "magnetic proximity model" proposed by Slonczewski is evaluated.Comment: 8 pages, 8 figure

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

Triangle-generation in topological D-brane categories

Tachyon condensation in topological Landau-Ginzburg models can generally be studied using methods of commutative algebra and properties of triangulated categories. The efficiency of this approach is demonstrated by explicitly proving that every D-brane system in all minimal models of type ADE can be generated from only one or two fundamental branes.Comment: 34 page

Insolubility of Mg in Β-Si 3 N 4 in the System Al-Mg-Si-O-N

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65816/1/j.1151-2916.1978.tb09345.x.pd

Massive star formation around I05345+3157 -- I. The dense gas

We present observations of the intermediate to massive star-forming region I05345+3157 using the molecular line tracer CS(2-1) with CARMA to reveal the properties of the dense gas cores. Seven gas cores are identified in the integrated intensity map of CS(2-1). Among these, core 1 and core 3 have counterparts in the 2.7 millimeter continuum data. We suggest that core 1 and core 3 are star-forming cores that may already or will very soon harbor young massive protostars. The total masses of core 1 estimated from the LTE method and dust emission by assuming a gas-to-dust ratio are 5 +- 1 solar masses and 18 +- 6 solar masses, and that of core 3 are 15 +- 7 solar masses and 11 +- 3 solar masses. The spectrum of core 3 shows blue-skewed self-absorption, which suggests gas infall -- a collapsing core. The observed broad linewidths of the seven gas cores indicate non-thermal motions. These non-thermal motions can be interactions with nearby outflows or due to the initial turbulence; the former is observed, while the role of initial turbulence is less certain. Finally, the virial masses of the gas cores are larger than the LTE masses, which for a bound core implies a requirement on the external pressure of ~ 10^8 K/cm^3. The cores have the potential to further form massive stars.Comment: Accepted for publication in MNRA