Search results for "Vector"
showing 10 items of 2660 documents
An Introduction to Hodge Structures
2015
We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of Hodge structures defined on their cohomology, and discuss its properties. This will lead us to the more general definition of a variation of Hodge structure and the Gauss-Manin connection. We then review the basics about mixed Hodge structures with a view towards degenerations of Hodge structures; including the canonical extension of a vector bundle with connection, Schmid’s limiting mixed Hodge structure and Steenbrink’s work in the geometric setting. Fin…
The deformation multiplicity of a map germ with respect to a Boardman symbol
2001
We define the deformation multiplicity of a map germ f: (Cn, 0) → (Cp, 0) with respect to a Boardman symbol i of codimension less than or equal to n and establish a geometrical interpretation of this number in terms of the set of Σi points that appear in a generic deformation of f. Moreover, this number is equal to the algebraic multiplicity of f with respect to i when the corresponding associated ring is Cohen-Macaulay. Finally, we study how algebraic multiplicity behaves with weighted homogeneous map germs.
Integration on Surfaces
2012
We intend to study the integration of a differential k-form over a regular k-surface of class C 1 in \(\mathbb{R}^n\). To begin with, in Sect. 7.1, we undertake the integration over a portion of the surface that is contained in a coordinate neighborhood. Where possible, we will express the obtained results in terms of integration of vector fields. For example, we study the integral of a vector field on a portion of a regular surface in \(\mathbb{R}^3\) and also the integral over a portion of a hypersurface in \(\mathbb{R}^n\). In Sect. 7.3 we study the integration of differential k-forms on regular k-surfaces admitting a finite atlas.We discuss the need for the surface to be orientable so t…
Techniques in the Theory of Local Bifurcations: Cyclicity and Desingularization
1993
A fundamental open question of the bifurcation theory of vector fields in dimension 2 is whether the number of locally bifurcating limit cycles in an analytic unfolding is bounded, or more precisely, whether any limit periodic set has finite cyclicity. In these notes we introduce several techniques for attacking this question: asymptotic expansion of return maps, ideal of coefficients, desingularization of parametrized families. Moreover, because of their practical interest, we present some partial results obtained by these techniques.
A Tomographical Characterization of L-convex Polyominoes
2005
Our main purpose is to characterize the class of L-convex polyominoes introduced in [3] by means of their horizontal and vertical projections. The achieved results allow an answer to one of the most relevant questions in tomography i.e. the uniqueness of discrete sets, with respect to their horizontal and vertical projections. In this paper, by giving a characterization of L-convex polyominoes, we investigate the connection between uniqueness property and unimodality of vectors of horizontal and vertical projections. In the last section we consider the continuum environment; we extend the definition of L-convex set, and we obtain some results analogous to those for the discrete case.
Kurzweil-Henstock type integration on Banach spaces
2004
In this paper properties of Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrals for vector-valued functions are studied. In particular, the absolute integrability for Kurzweil-Henstock integrable functions is characterized and a Kurzweil-Henstock version of the Vitali Theorem for Pettis integrable functions is given.
Stability of the fixed point property in Hilbert spaces
2005
In this paper we prove that if X X is a Banach space whose Banach-Mazur distance to a Hilbert space is less than 5 + 17 2 \sqrt {\frac {5+\sqrt {17}}{2}} , then X X has the fixed point property for nonexpansive mappings.
On stability of logarithmic tangent sheaves. Symmetric and generic determinants
2021
We prove stability of logarithmic tangent sheaves of singular hypersurfaces D of the projective space with constraints on the dimension and degree of the singularities of D. As main application, we prove that determinants and symmetric determinants have stable logarithmic tangent sheaves and we describe an open dense piece of the associated moduli space.
Group-symmetric holomorphic functions on a Banach space
2016
We study the holomorphic functions on a complex Banach space E that are invariant under the action of a given group of operators on E. A great variety of situations occur depending, of course, on the group and the space. Nevertheless, in the examples we deal with, they can be described in terms of a few natural ones and functions of a finite number of variables. Fil: Aron, Richard. Universidad de Valencia; España Fil: Galindo, Pablo. Universidad de Valencia; España Fil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Zalduendo, Ignacio Martin. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de I…
Supermanifolds, Symplectic Geometry and Curvature
2016
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.