Search results for "MSC: Primary"

showing 10 items of 16 documents

Moduli spaces of rank two aCM bundles on the Segre product of three projective lines

2016

Let P^n be the projective space of dimension n on an algebraically closed field of characteristic 0 and F be the image of the Segre embedding of P^1xP^1xP^1 inside P^7. In the present paper we deal with the moduli spaces of locally free sheaves E on F of rank 2 with h^i(F,E(t))=0 for i=1,2 and each integer t.

14J60 14J45 14D20[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]Rank (differential topology)Commutative Algebra (math.AC)01 natural sciences[ MATH.MATH-AC ] Mathematics [math]/Commutative Algebra [math.AC]CombinatoricsMathematics - Algebraic GeometryMathematics::Algebraic Geometry0103 physical sciencesFOS: Mathematics0101 mathematicsProjective testAlgebraic Geometry (math.AG)MathematicsAlgebra and Number TheoryImage (category theory)010102 general mathematicsMathematics - Commutative Algebra16. Peace & justice[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Moduli spaceSegre embeddingMSC: Primary: 14J60; secondary: 14J45; 14D20Product (mathematics)[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physicsJournal of Pure and Applied Algebra
researchProduct

Rank two aCM bundles on the del Pezzo fourfold of degree 6 and its general hyperplane section

2018

International audience; In the present paper we completely classify locally free sheaves of rank 2 with vanishing intermediate cohomology modules on the image of the Segre embedding $\mathbb{P}^2$ x $\mathbb{P}^2 \subseteq \mathbb{P}^8$ and its general hyperplane sections.Such a classification extends similar already known results regarding del Pezzo varieties with Picard numbers 1 and 3 and dimension at least 3.

Algebra and Number TheoryDegree (graph theory)Image (category theory)010102 general mathematicsDimension (graph theory)MSC: Primary 14J60 ; secondary 14J45Hyperplane sectionRank (differential topology)01 natural sciencesCohomologySegre embedding[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]CombinatoricsAlgebraMathematics::Algebraic GeometryHyperplane0103 physical sciences010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsMathematics
researchProduct

Triple planes with $p_g=q=0$

2019

We show that general triple planes with p_g=q=0 belong to at most 12 families, that we call surfaces of type I,..., XII, and we prove that the corresponding Tschirnhausen bundle is direct sum of two line bundles in cases I, II, III, whereas is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit constructions for surfaces of type I,..., VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski.

Discrete mathematicsSteiner bundleApplied MathematicsGeneral Mathematics010102 general mathematicsprojective varietiesspaceadjunction theorysurfaces01 natural sciences14E20bundlesunstable hyperplanesMathematics - Algebraic GeometryTriple plane0103 physical sciencesFOS: Mathematics010307 mathematical physicsarrangements[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsMSc: Primary 14E20 14J60Algebraic Geometry (math.AG)Mathematicscovers
researchProduct

Lyapunov graphs for circle valued functions

2018

International audience; Conley index theory is used to obtain results for flows associated to circular Lyapunov functions defined on general compact smooth n-manifolds. This is done in terms of their underlying circular Lyapunov digraphs, which are generalizations of Morse digraphs, by extensively studying their combinatorics, invariants and realizability.

Lyapunov functionNovikov theoryPure mathematicsMathematics::Dynamical Systems010102 general mathematicsTEORIA DO ÍNDICEMorse code01 natural scienceslaw.inventionLyapunov graphs010101 applied mathematicssymbols.namesakeMorse functions[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]lawRealizabilitysymbolsGeometry and TopologyConley index theory0101 mathematicsMathematics::Symplectic GeometryGeneric circularMSC: primary 37B30 37B35 37D15 secondary 37E35MathematicsConley index
researchProduct

The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras

2016

We describe completely the link invariants constructed using Markov traces on the Yokonuma-Hecke algebras in terms of the linking matrix and the HOMFLYPT polynomials of sublinks.

MSC: Primary 57M27: Invariants of knots and 3-manifolds Secondary 20C08: Hecke algebras and their representations 20F36: Braid groups; Artin groups 57M25: Knots and links in $S^3$Pure mathematicsMarkov chainGeneral Mathematics010102 general mathematicsYokonuma-Hecke algebrasGeometric Topology (math.GT)Linking numbers01 natural sciencesMathematics::Geometric TopologyMatrix (mathematics)Mathematics - Geometric TopologyMarkov tracesMathematics::Quantum Algebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)010307 mathematical physics0101 mathematicsRepresentation Theory (math.RT)Link (knot theory)Mathematics - Representation TheoryMathematics
researchProduct

The forgotten mathematical legacy of Peano

2019

International audience; The formulations that Peano gave to many mathematical notions at the end of the 19th century were so perfect and modern that they have become standard today. A formal language of logic that he created, enabled him to perceive mathematics with great precision and depth. He described mathematics axiomatically basing the reasoning exclusively on logical and set-theoretical primitive terms and properties, which was revolutionary at that time. Yet, numerous Peano’s contributions remain either unremembered or underestimated.

PeanoPeano's axioms of arithmeticPeano's counterexamplesWeierstrass maximum theoremabstract measuresGeneral MathematicsClosure (topology)tangencyinterioranti-distributive familiesfoundationdefinitions by abstractionlinear differential equationsaxiom of choiceLogical conjunctionPeano axiomsproofFormal languageAxiom of choiceMSC: Primary 01A55 01A6003-03 26-03 28-03 34-03 54-03; Secondary15A75 26A03 26A2426B25 26B05 28A1228A15 28A75.affine exterior algebra[MATH]Mathematics [math]reduction formulaeMathematicsnonlinear differential equationsoptimality conditionsdifferentiation of measuressweeping-tangent theoremPeano's axioms of geometryPeano's filling curvereduction of mathematics to setssurface areaclosuremean value theoremDirichlet functionNonlinear differential equationssubtangentsEpistemologymeasure theoryplanar measurelower and upper limits of setsdistributive familiescompactnessmathematical definitions1886 existence theoremdifferentiabilityDissertationes Mathematicae
researchProduct

Locally nilpotent derivations of rings graded by an abelian group

2019

International audience

Russel cubic threefoldPure mathematicsAffine algebraic geometryPham-Brieskorn variety010102 general mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Locally nilpotent13A50Locally nilpotent derivation01 natural sciences[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Russell cubic threefold0103 physical sciences010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsAbelian group14R20MSC: Primary 14R20 ; Secondary 13A50ComputingMilieux_MISCELLANEOUSMathematics
researchProduct

Module categories of finite Hopf algebroids, and self-duality

2017

International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.

Self-duality[ MATH ] Mathematics [math]Finite tensor categoryGeneral MathematicsDuality (mathematics)Representation theory of Hopf algebrasBimodulesQuasitriangular Hopf algebra01 natural sciencesMonoidal CategoriesMathematics::Category TheoryMathematics::Quantum Algebra0103 physical sciencesRings0101 mathematicsAlgebra over a fieldAbelian group[MATH]Mathematics [math]Fusion categoryHopf algebroidMSC: Primary 16T99 18D10SubfactorsMathematicsQuantum groupApplied Mathematics010102 general mathematicsMathematics::Rings and AlgebrasTensor CategoriesTheorem16. Peace & justiceHopf algebraDual (category theory)Algebra010307 mathematical physicsWeak Hopf algebra
researchProduct

Seifert manifolds admitting partially hyperbolic diffeomorphisms

2017

We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.

Surface (mathematics)Pure mathematicsMathematics::Dynamical SystemsCircle bundle[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)01 natural sciences[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]0103 physical sciencesFOS: MathematicsMSC: Primary: 37D30 37C15; Secondary: 57R30 55R05.Mathematics - Dynamical Systems0101 mathematicsMathematics::Symplectic GeometrySeifert spacesMathematics - General TopologyMathematicsTransitive relationAlgebra and Number TheoryApplied Mathematics010102 general mathematicsGeneral Topology (math.GN)Mathematics::Geometric TopologyFlow (mathematics)Partially hyperbolic diffeomorphisms010307 mathematical physicsDiffeomorphismAnalysis
researchProduct

A remark on hyperplane sections of rational normal scrolls

2017

We present algebraic and geometric arguments that give a complete classification of the rational normal scrolls that are hyperplane section of a given rational normal scrolls.

TheoryofComputation_MISCELLANEOUSMathematics::Commutative AlgebraInformationSystems_INFORMATIONINTERFACESANDPRESENTATION(e.g.HCI)Determinantal idealsMSC: Primary 14M12 13C40Quantitative Biology::Tissues and Organs[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Commutative AlgebraCommutative Algebra (math.AC)[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Algebraic GeometryComputingMethodologies_PATTERNRECOGNITIONMathematics::Algebraic GeometryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComputingMethodologies_DOCUMENTANDTEXTPROCESSINGFOS: MathematicsRational normal scrolls[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Nonlinear Sciences::Pattern Formation and SolitonsAlgebraic Geometry (math.AG)
researchProduct