-pseudoconvex and -complete domains
q-completeness and q-concavity of the union of open subspaces.
q-Completeness of Subsets in Complex Projective Space.
q-konvexe Restmengen in kompakten komplexen Mannigfaltigkeiten.
q-plurisubharmonicity and q-pseudoconvexity in Cn.
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 Holomorphic Foliations on Singular Surfaces.
Quadratic forms and singularities of genus one or two
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
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.
Quadratintegrable holomorphe Funktionen und die Serre-Vermutung.
Quadratische Formen und Monodromiegruppen von Singularitäten.
Qualche riflessione sulla rappresentazione integrale di massima dimensione per le funzioni di più variabili complesse.
Another aspect of the representation formula is given.
Quantifier elimination in quasianalytic structures via non-standard analysis
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
This paper investigates the geometry of the expansion 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 in the language ℒ augmented by the names of rational powers. Our approach makes no appeal to the Weierstrass preparation...
Quantitative Bloch's theorem for certain classes of holomorphic mappings of the ball into Pn (C).
Quantitative estimates for the Green function and an application to the Bergman metric
Let be a bounded pseudoconvex domain that admits a Hölder continuous plurisubharmonic exhaustion function. Let its pluricomplex Green function be denoted by . In this article we give for a compact subset a quantitative upper bound for the supremum in terms of the boundary distance of and . This enables us to prove that, on a smooth bounded regular domain (in the sense of Diederich-Fornaess), the Bergman differential metric tends to infinity, for , when tends to a boundary point....
Quantum Cohomology and Periods
In a previous paper, the author introduced an integral structure in quantum cohomology defined by the -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 integrable model of an arrangement of hyperplanes.
Quantum Singularity Theory for and -Spin Theory
We give a review of our construction of a cohomological field theory for quasi-homogeneous singularities and the -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity of type our construction of the stack of -curves is canonically isomorphic to the stack of -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine proof of the...
Quasialgebraic functions
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).