Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings

Cyclotomic Curve Families over Elliptic Curves with Complete Picard-Einstein Metric

According to a problem of Hirzebruch we look for models of biproducts of elliptic CM-curves with Picard modular structure. We introduce the singular mean value of crossing elliptic divisors on surfaces and determine its maximum for all abelian surfaces. For any maximal crossing elliptic divisor on an abelian surface A we construct infinite towers of coverings of A whose members, inclusively A, are contracted compactified ball quo- tients. On this way we find towers of Picard modular surfaces of the Gauss number field including E × E blown up at six points (E \cong C/Z[i]), the Kummer surface of the rational cuboid problem (3-dimensional extension of congruence number problem) and some interesting rational surfaces together with the corresponding congruence subgroups of U((2,1),Z[i])

Taxonomic study of Weissella confusa and description of Weissella cibaria sp. nov., detected in food and clinical samples

http://ijs.sgmjournals.org/A taxonomic study was conducted in order to clarify the relationships of two bacterial populations belonging to the genus Weissella. A total of 39 strains originating mainly from Malaysian foods (22 strains) and clinical samples from humans (9 strains) and animals (6 strains) were analysed using a polyphasic taxonomic approach. The methods included classical phenotyping, whole-cell protein electrophoresis, 16S and 23S rDNA RFLP (ribotyping), the determination of 16S rDNA sequence homologies, and DNA-DNA reassociation levels. Based on the results, the strains were considered to represent two different species, Weissella confusa and a novel Weissella species, for which we propose the name Weissella cibaria sp. nov. W. confusa possessed the highest 16S rDNA sequence similarity to W. cibaria sp. nov. but the DNA-DNA reassociation experiment showed hybridisation levels below 49% between the strains studied. The numerical analyses of W. confusa and W. cibaria sp. nov. strains did not reveal any specific clustering with respect to the origin of the strains. Based on whole cell protein electrophoresis, ClaI and HindIII ribotyping patterns, food and clinical isolates were randomly located in the two species-specific clusters obtained

Characterization of Leuconostoc gasicomitatum sp. nov., Associated with Spoiled Raw Tomato-Marinated Broiler Meat Strips Packaged under Modified-Atmosphere Conditions

http://aem.asm.org/Lactic acid bacteria (LAB) associated with gaseous spoilage of modified-atmosphere-packaged, raw, tomatomarinated broiler meat strips were identified on the basis of a restriction fragment length polymorphism (RFLP) (ribotyping) database containing DNAs coding for 16S and 23S rRNAs (rDNAs). A mixed LAB population dominated by a Leuconostoc species resembling Leuconostoc gelidum caused the spoilage of the product. Lactobacillus sakei, Lactobacillus curvatus, and a gram-positive rod phenotypically similar to heterofermentative Lactobacillus species were the other main organisms detected. An increase in pH together with the extreme bulging of packages suggested a rare LAB spoilage type called “protein swell.” This spoilage is characterized by excessive production of gas due to amino acid decarboxylation, and the rise in pH is attributed to the subsequent deamination of amino acids. Protein swell has not previously been associated with any kind of meat product. A polyphasic approach, including classical phenotyping, whole-cell protein electrophoresis, 16 and 23S rDNA RFLP, 16S rDNA sequence analysis, and DNA-DNA reassociation analysis, was used for the identification of the dominant Leuconostoc species. In addition to the RFLP analysis, phenotyping, whole-cell protein analysis, and 16S rDNA sequence homology indicated that L. gelidum was most similar to the spoilage-associated species. The two spoilage strains studied possessed 98.8 and 99.0% 16S rDNA sequence homology with the L. gelidum type strain. DNA-DNA reassociation, however, clearly distinguished the two species. The same strains showed only 22 and 34% hybridization with the L. gelidum type strain. These results warrant a separate species status, and we propose the name Leuconostoc gasicomitatum sp. nov. for this spoilage-associated Leuconostoc species

Characterization of Leuconostoc gasicomitatum sp. nov., Associated with Spoiled Raw Tomato-Marinated Broiler Meat Strips Packaged under Modified-Atmosphere Conditions

http://aem.asm.org/Lactic acid bacteria (LAB) associated with gaseous spoilage of modified-atmosphere-packaged, raw, tomatomarinated broiler meat strips were identified on the basis of a restriction fragment length polymorphism (RFLP) (ribotyping) database containing DNAs coding for 16S and 23S rRNAs (rDNAs). A mixed LAB population dominated by a Leuconostoc species resembling Leuconostoc gelidum caused the spoilage of the product. Lactobacillus sakei, Lactobacillus curvatus, and a gram-positive rod phenotypically similar to heterofermentative Lactobacillus species were the other main organisms detected. An increase in pH together with the extreme bulging of packages suggested a rare LAB spoilage type called “protein swell.” This spoilage is characterized by excessive production of gas due to amino acid decarboxylation, and the rise in pH is attributed to the subsequent deamination of amino acids. Protein swell has not previously been associated with any kind of meat product. A polyphasic approach, including classical phenotyping, whole-cell protein electrophoresis, 16 and 23S rDNA RFLP, 16S rDNA sequence analysis, and DNA-DNA reassociation analysis, was used for the identification of the dominant Leuconostoc species. In addition to the RFLP analysis, phenotyping, whole-cell protein analysis, and 16S rDNA sequence homology indicated that L. gelidum was most similar to the spoilage-associated species. The two spoilage strains studied possessed 98.8 and 99.0% 16S rDNA sequence homology with the L. gelidum type strain. DNA-DNA reassociation, however, clearly distinguished the two species. The same strains showed only 22 and 34% hybridization with the L. gelidum type strain. These results warrant a separate species status, and we propose the name Leuconostoc gasicomitatum sp. nov. for this spoilage-associated Leuconostoc species

Jacobi theta embedding of a hyperbolic 4-space with cusps

Starting from a fixed elliptic curve with complex multiplication we compose lifted quotients of elliptic Jacobi theta functions to abelian functions in higher dimension. In some cases, where complete Picard-Einstein metrics have been discovered on the underlying abelian surface (outside of cusp points), we are able to transform them to Picard modular forms. Basic algebraic relations of basic forms come from different multiplicative decompositions of these abelian functions in simple ones of the same lifted type. In the case of Gauss numbers the constructed basic modular forms define a Baily-Borel embedding in P22. The relations yield explicit homogeneous equations for the Picard modular image surface

Orbital Functional Series on Picard Surfaces

We introduce orbital functionals $\int \boldsymbol{\beta}$ simultaneously for each commensurability class of orbital surfaces. They are realized on infinitely dimensional \emph{orbital} divisor spaces spanned by (arithmetic-geodesic real $2$-dimensional) orbital curves on any orbital surface. We discover infinitely many of them on each commensurability class of orbital Picard surfaces, which are real $4$-spaces with cusps and negative constant Kähler-Einstein metric degenerated along an orbital cycle. For a suitable (Heegner) sequence $\int \mathbf{h}_N$, $N \in \mathbb{N}$, of them we investigate the corresponding formal orbital $q$-series $\mathop{\sum}\limits_{N=0}^\infty (\int \mathbf{\mathbf{h}}_N)q^N$. We show that after substitution q = \re^{2\pi\ri\tau} and application to arithmetic orbital curves $\mathbf{\hat{C}}$ on a fixed Picard surface class the series \mathop{\sum}\limits_{N=0}^{\infty} (\int_{\mathbf{\hat{C}}} \mathbf{\mathbf{h}}_N)\re^{2\pi\ri\tau} define modular forms of well-determined fixed weight, level and Nebentypus. The proof needs a new orbital understan-ding of orbital hights introduced in \cite{Ho1} and Mumford-Fulton's rational intersection theory on singular surfaces in Riemann-Roch-Hirzebruch style. It has to be connected with Zeta and Theta functions of hermitian lines, indefinit quaternionic fields and of a matrix algebra along a research marathon over $75$ years represented by Cogdell, Kudla, Hirzebruch, Zagier, Shimura, Schoeneberg and Hecke. Our aim is to open a door to an effective enumerative geometry for complex geodesics on orbital varieties with nice metrics

Picard-Einstein Metrics and Class Fields Connected with Apollonius Cycle

We define Picard_Einstein metrics on complex algebraic surfaces as Kähler-Einstein metrics with negative constant sectional curvature pushed down from the unit ball via Picard modular groups allowing degenerations along cycles. We demonstrate how the tool of orbital heights, especially the Proportionality Theorem presented in [H98], works for detecting such orbital cycles on the projective plane. The simplest cycle we found on this way is supported by a quadric and three tangent lines (Apollonius configuration). We give a complete proof for the fact that it belongs to the congruence subgroup of level 1 + i of the full Picard modular group of Gauß numbers together with precise octahedral- symmetric interpretation as moduli space of an explicit Shimura family of curves of genus 3. Proofs are based only on the Proportionality Theorem and classification results for hermitian lattices and algebraic surfaces

Abelian approach to modular forms of neat 2-ball lattices

In previous papers [HoEis], [Ho2000] we found neat Picard modular surfaces with abelian minimal model and, conversely, a divisor criterion on abelian surfaces A for such a situation. For the corresponding ball lattices Gamma we prove dimension formulas for modular forms depending only on the intersection graph of the image on A of the compactification divisor of the Gamma-quotient surface