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q-plurisubharmonicity and q-pseudoconvexity in Cn.

Nguyen Quang Dieu (2006)

Publicacions Matemàtiques

We generalize classical results for plurisubharmonic functions and hyperconvex domain to q-plurisubharmonic functions and q-hyperconvex domains. We show, among other things, that Bq-regular domains are q-hyperconvex. Moreover, some smoothing results for q-plurisubharmonic functions are also given.

Quadratic forms and singularities of genus one or two

Georges Dloussky (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We study singularities obtained by the contraction of the maximal divisor in compact (non-kählerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be -Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting coefficient of a non-vanishing...

Quadratic mappings and configuration spaces

Gia Giorgadze (2003)

Banach Center Publications

We discuss some approaches to the topological study of real quadratic mappings. Two effective methods of computing the Euler characteristics of fibers are presented which enable one to obtain comprehensive results for quadratic mappings with two-dimensional fibers. As an illustration we obtain a complete topological classification of configuration spaces of planar pentagons.

Quantifier elimination in quasianalytic structures via non-standard analysis

Krzysztof Jan Nowak (2015)

Annales Polonici Mathematici

The paper is a continuation of an earlier one where we developed a theory of active and non-active infinitesimals and intended to establish quantifier elimination in quasianalytic structures. That article, however, did not attain full generality, which refers to one of its results, namely the theorem on an active infinitesimal, playing an essential role in our non-standard analysis. The general case was covered in our subsequent preprint, which constitutes a basis for the approach presented here....

Quantifier elimination, valuation property and preparation theorem in quasianalytic geometry via transformation to normal crossings

Krzysztof Jan Nowak (2009)

Annales Polonici Mathematici

This paper investigates the geometry of the expansion Q of the real field ℝ by restricted quasianalytic functions. The main purpose is to establish quantifier elimination, description of definable functions by terms, the valuation property and preparation theorem (in the sense of Parusiński-Lion-Rolin). To this end, we study non-standard models of the universal diagram T of Q in the language ℒ augmented by the names of rational powers. Our approach makes no appeal to the Weierstrass preparation...

Quantitative estimates for the Green function and an application to the Bergman metric

Klas Diederich, Gregor Herbort (2000)

Annales de l'institut Fourier

Let D n be a bounded pseudoconvex domain that admits a Hölder continuous plurisubharmonic exhaustion function. Let its pluricomplex Green function be denoted by G D ( . , . ) . In this article we give for a compact subset K D a quantitative upper bound for the supremum sup z K | G D ( z , w ) | in terms of the boundary distance of K and w . This enables us to prove that, on a smooth bounded regular domain D (in the sense of Diederich-Fornaess), the Bergman differential metric B D ( w ; X ) tends to infinity, for X n / { O } , when w D tends to a boundary point....

Quantum Cohomology and Periods

Hiroshi Iritani (2011)

Annales de l’institut Fourier

In a previous paper, the author introduced an integral structure in quantum cohomology defined by the K -theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle to the previous results, we find an explicit relationship between solutions to the quantum differential equation of toric complete intersections and the periods (or oscillatory integrals) of their mirrors. We describe in detail the mirror isomorphism of...

Quantum Singularity Theory for A ( r - 1 ) and r -Spin Theory

Huijun Fan, Tyler Jarvis, Yongbin Ruan (2011)

Annales de l’institut Fourier

We give a review of our construction of a cohomological field theory for quasi-homogeneous singularities and the r -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity W of type A our construction of the stack of W -curves is canonically isomorphic to the stack of r -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an r -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine proof of the...

Quasialgebraic functions

G. Binyamini, D. Novikov, S. Yakovenko (2011)

Banach Center Publications

We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated zeros can be explicitly counted. On the other hand, this class is sufficiently rich to include all periods (integral of rational forms over algebraic cycles).

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