Laurent Polynomials, GKZ-hypergeometric Systems and Mixed Hodge Modules

Given a family of Laurent polynomials, we will construct a morphism between its (proper) Gauss-Manin system and a direct sum of associated GKZ systems. The kernel and cokernel of this morphism are very simple and consist of free O-modules. The result above enables us to put a mixed Hodge module structure on certain classes of GKZ systems and shows that they have quasi-unipotent monodromy.Comment: 34 page

Logarithmic degenerations of Landau-Ginzburg models for toric orbifolds and global tt^* geometry

We discuss the behavior of Landau-Ginzburg models for toric orbifolds near the large volume limit. This enables us to express mirror symmetry as an isomorphism of Frobenius manifolds which aquire logarithmic poles along a boundary divisor. If the toric orbifold admits a crepant resolution we construct a global moduli space on the B-side and show that the associated tt^*-geometry exists globally.Comment: 40 page

On the bb-functions of hypergeometric systems

For any integer $d\times (n+1)$ matrix $A$ and parameter \beta\in\CC^d let $M_A(\beta)$ be the associated $A$-hypergeometric (or GKZ) system in the variables $x_0,\ldots,x_n$. We describe bounds for the (roots of the) $b$-functions of both $M_A(\beta)$ and its Fourier transform along the hyperplanes $(x_j=0)$. We also give an estimate for the $b$-function for restricting $M_A(\beta)$ to a generic point.Comment: 14 pages, several figures. Typos correcte

Logarithmic Frobenius manifolds, hypergeometric systems and quantum D-modules

We describe mirror symmetry for weak toric Fano manifolds as an equivalence of D-modules equipped with certain filtrations. We discuss in particular the logarithmic degeneration behavior at the large radius limit point, and express the mirror correspondence as an isomorphism of Frobenius manifolds with logarithmic poles. The main tool is an identification of the Gauss-Manin system of the mirror Landau-Ginzburg model with a hypergeometric D-module, and a detailed study of a natural filtration defined on this differential system. We obtain a solution of the Birkhoff problem for lattices defined by this filtration and show the existence of a primitive form, which yields the construction of Frobenius structures with logarithmic poles associated to the mirror Laurent polynomial. As a final application, we show the existence of a pure polarized non-commutative Hodge structure on a Zariski open subset of the complexified Kaehler moduli space of the variety

A construction of Frobenius manifolds with logarithmic poles and applications

A construction theorem for Frobenius manifolds with logarithmic poles is established. This is a generalization of a theorem of Hertling and Manin. As an application we prove a generalization of the reconstruction theorem of Kontsevich and Manin for projective smooth varieties with convergent Gromov-Witten potential. A second application is a construction of Frobenius manifolds out of a variation of polarized Hodge structures which degenerates along a normal crossing divisor when certain generation conditions are fulfilled.Comment: 46 page

Analyzing the actions of the Administration of Novy Vasyugan rural settlement

The paper analyzes the actions of the Administration of Novy Vasyugan rural settlement. Novy Vasyugan is a village in Tomsk oblast and an administrative center of rural settlement. The Administration is a key element of a democratic society. Every citizen deals with an administration. Nowadays it is developing and legislative branch does not work in a perfect way as its financial and economic resources are limited. The paper describes the structure of rural administration: the duties of municipal bodies, its rights. The goals and results of Novy Vasyugan municipal programs are described: socio-economic growth plan, fire safety municipal target program, energy efficiency municipal target program and antiextremism complex municipal program