Search results for " Geometry"

showing 10 items of 2294 documents

Linear quotients of Artinian Weak Lefschetz algebras

2013

Abstract We study the Hilbert function and the graded Betti numbers for “generic” linear quotients of Artinian standard graded algebras, especially in the case of Weak Lefschetz algebras. Moreover, we investigate a particular property of Weak Lefschetz algebras, the Betti Weak Lefschetz Property, which makes possible to completely determine the graded Betti numbers of a generic linear quotient of such algebras.

Discrete mathematicsPure mathematicsHilbert series and Hilbert polynomialAlgebra and Number TheoryProperty (philosophy)Mathematics::Commutative AlgebraBetti numberBetti Weak Lefschetz PropertyMathematics::Rings and AlgebrasArtinian algebraLinear quotientWeak Lefschetz Propertysymbols.namesakeQuotientWeak Lefschetz; Artinian algebra; QuotientsymbolsWeak Lefschetz Property Artinian algebra Linear quotientLefschetz fixed-point theoremWeak LefschetzMathematics::Symplectic GeometryQuotientMathematics
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Geometric properties of involutive distributions on graded manifolds

1997

AbstractA proof of the relative version of Frobenius theorem for a graded submersion, which includes a very short proof of the standard graded Frobenius theorem is given. Involutive distributions are then used to characterize split graded manifolds over an orientable base, and split graded manifolds whose Batchelor bundle has a trivial direct summand. Applications to graded Lie groups are given.

Discrete mathematicsPure mathematicsMathematics(all)Mathematics::Commutative AlgebraGeneral MathematicsMathematics::Rings and AlgebrasLie groupGraded Lie algebrasymbols.namesakeDifferential graded algebraBundlesymbolsMathematics::Differential GeometryFrobenius theorem (differential topology)MathematicsIndagationes Mathematicae
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Holomorphically ultrabornological spaces and holomorphic inductive limits

1987

Abstract The holomorphically ultrabornological spaces are introduced. Their relation with other holomorphically significant classes of locally convex spaces is established and separating examples are given. Some apparently new properties of holomorphically barrelled spaces are included and holomorphically ultrabornological spaces are utilized in a problem posed by Nachbin.

Discrete mathematicsPure mathematicsMathematics::Complex VariablesApplied MathematicsLocally convex topological vector spaceHolomorphic functionMathematics::Symplectic GeometryAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Topological classification of gradient-like diffeomorphisms on 3-manifolds

2004

Abstract We give a complete invariant, called global scheme , of topological conjugacy classes of gradient-like diffeomorphisms, on compact 3-manifolds. Conversely, we can realize any abstract global scheme by such a diffeomorphism.

Discrete mathematicsPure mathematicsMathematics::Dynamical SystemsTopological classificationTopological classificationGeometry and TopologyDiffeomorphismInvariant (mathematics)Topological conjugacyMathematics::Symplectic GeometryMorse–Smale diffeomorphismsMathematics3-manifoldsTopology
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Best proximity point theorems for rational proximal contractions

2013

Abstract We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results. MSC:41A65, 46B20, 47H10.

Discrete mathematicsPure mathematicsMetric spaceDifferential geometrySettore MAT/05 - Analisi MatematicaApplied MathematicsProximity problemsUniquenessGeometry and TopologyFixed pointPoint theorybest proximity point contraction fixed point generalized proximal contraction optimal approximate solutionMathematicsFixed Point Theory and Applications
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Spectral invariance, ellipticity, and the Fredholm property for pseudodifferential operators on weighted Sobolev spaces

1992

The pseudodifferential operators with symbols in the Grushin classes \~S inf0 supρ,δ , 0 ≤ δ < ρ ≤ 1, of slowly varying symbols are shown to form spectrally invariant unital Frecher-*-algebras (Ψ*-algebras) in L(L 2(R n )) and in L(H γ st ) for weighted Sobolev spaces H infγ sup defined via a weight d function γ. In all cases, the Fredholm property of an operator can be characterized by uniform ellipticity of the symbol. This gives a converse to theorems of Grushin and Kumano-Ta-Taniguchi. Both, the spectrum and the Fredholm spectrum of an operator turn out to be independent of the choices of s, t and γ. The characterization of the Fredholm property by uniform ellipticity leads to an index …

Discrete mathematicsPure mathematicsParametrixFredholm integral equationCompact operatorFredholm theorySobolev spacesymbols.namesakeOperator (computer programming)Differential geometryMathematics::K-Theory and HomologysymbolsGeometry and TopologyAtiyah–Singer index theoremAnalysisMathematicsAnnals of Global Analysis and Geometry
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Projective spaces on partially ordered sets and Desargues' postulate

1991

We introduce a generalized concept of projective and Desarguean space where points (and lines) may be of different size. Every unitary module yields an example when we take the 1-and 2-generated submodules as points and lines. In this paper we develop a method of constructing a wide range of projective and Desarguean spaces by means of lattices.

Discrete mathematicsPure mathematicsProjective harmonic conjugateCollineationComplex projective spaceProjective spaceGeometry and TopologyProjective planeQuaternionic projective spaceNon-Desarguesian planeProjective geometryMathematicsGeometriae Dedicata
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A unified approach to projective lattice geometries

1992

The interest in pursuing projective geometry on modules has led to several lattice theoretic generalizations of the classical synthetic concept of projective geometry on vector spaces.

Discrete mathematicsPure mathematicsProjective harmonic conjugateCollineationDuality (projective geometry)Projective spaceErlangen programGeometry and TopologyProjective differential geometryPencil (mathematics)MathematicsProjective geometryGeometriae Dedicata
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Embedding linear spaces with two line degrees in finite projective planes

1986

In this paper we shall classify all finite linear spaces with line degrees n and n-k having at most n2+n+1 lines. As a consequence of this classification it follows: If n is large compared with k, then any such linear space can be embedded in a projective plane of order n−1 or n.

Discrete mathematicsPure mathematicsReal projective lineReal projective planeDuality (projective geometry)Finite geometryProjective spaceLine at infinityGeometry and TopologyFano planeProjective planeMathematicsJournal of Geometry
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Elementary (-1)-curves of P-3

2006

In this note we deal with rational curves in P^3 which are images of a line by means of a finite sequence of cubo-cubic Cremona transformations. We prove that these curves can always be obtained applying to the line a sequence of such transformations increasing at each step the degree of the curve. As a corollary we get a result about curves that can give speciality for linear systems of P^3.

Discrete mathematicsSequenceAlgebra and Number TheoryDegree (graph theory)Linear system14C20Finite sequenceMathematics - Algebraic GeometryCorollaryLinear systems fat pointsFamily of curvesLine (geometry)FOS: MathematicsSettore MAT/03 - GeometriaAlgebraic Geometry (math.AG)Computer Science::DatabasesMathematics
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