Search results for " 14J60"

showing 8 items of 8 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
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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
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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
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Ulrich bundles on K3 surfaces

2019

We show that any polarized K3 surface supports special Ulrich bundles of rank 2.

Pure mathematics14J60Algebra and Number TheoryMathematics::Commutative Algebra13C1414F05 13C14 14J60 16G60010102 general mathematics14F05acm bundlesACM vector sheaves and bundlesK3 surfaces01 natural sciencesUlrich sheavesMathematics - Algebraic GeometryMathematics::Algebraic Geometry0103 physical sciencesFOS: Mathematicssheaves010307 mathematical physics0101 mathematicsmoduli[MATH]Mathematics [math]Algebraic Geometry (math.AG)Mathematics
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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.

Pure mathematicsLogarithmMSC 14J60 14J17 14M12 14C05General Mathematics[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]Commutative Algebra (math.AC)determinant01 natural sciencesStability (probability)Mathematics - Algebraic GeometryMathematics::Algebraic GeometryDimension (vector space)FOS: Mathematicsstability of sheavesProjective space0101 mathematicsAlgebraic Geometry (math.AG)MathematicsDegree (graph theory)010102 general mathematicsLogarithmic tangentTangentisolated singularitiesmoduli space of semistable sheavesMathematics - Commutative AlgebraModuli space010101 applied mathematicsGravitational singularityMathematics::Differential Geometry[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
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Truncated modules and linear presentations of vector bundles

2018

We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded Artinian modules with pure resolutions. Our method allows one to produce several new examples, and provides an alternative point of view on the existing ones.

Pure mathematicsRank (linear algebra)General Mathematics[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]Vector bundle010103 numerical & computational mathematicsLinear presentationCommutative Algebra (math.AC)01 natural sciences[ MATH.MATH-AC ] Mathematics [math]/Commutative Algebra [math.AC]Mathematics - Algebraic GeometryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsPoint (geometry)MSC: 13D02 16W50 15A30 14J600101 mathematicsVector bundleAlgebraic Geometry (math.AG)MathematicsMathematics::Commutative Algebra010102 general mathematicsConstruct (python library)Graded truncated moduleMathematics - Commutative AlgebraInstanton bundleCohomology[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Matrix of co nstant rank[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Constant (mathematics)
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Surfaces of minimal degree of tame representation type and mutations of Cohen–Macaulay modules

2017

We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands.

[ MATH ] Mathematics [math]Pure mathematicsFibonacci numberGeneral MathematicsType (model theory)Rank (differential topology)Commutative Algebra (math.AC)01 natural sciencesMathematics - Algebraic GeometryACM bundlesVarieties of minimal degreeMathematics::Algebraic Geometry0103 physical sciencesFOS: MathematicsMathematics (all)Rings0101 mathematics[MATH]Mathematics [math]Algebraic Geometry (math.AG)MathematicsDiscrete mathematics14F05 13C14 14J60 16G60010102 general mathematicsVarietiesMCM modulesACM bundles; MCM modules; Tame CM type; Ulrich bundles; Varieties of minimal degree; Mathematics (all)Ulrich bundlesMathematics - Commutative AlgebraQuintic functionElliptic curveTame CM typeProjective lineBundles010307 mathematical physicsIsomorphismIndecomposable moduleMSC: 14F05; 13C14; 14J60; 16G60
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An unbounded family of log Calabi–Yau pairs

2016

We give an explicit example of log Calabi-Yau pairs that are log canonical and have a linearly decreasing Euler characteristic. This is constructed in terms of a degree two covering of a sequence of blow ups of three dimensional projective bundles over the Segre-Hirzebruch surfaces ${\mathbb F}_n$ for every positive integer $n$ big enough.

geography of threefoldSequenceDegree (graph theory)Projective bundleGeneral Mathematics14J30 14J32 14J60CombinatoricsMathematics - Algebraic Geometrysymbols.namesakeMathematics::Algebraic Geometryprojective bundlesIntegerEuler characteristicLog Calabi-Yau pairFOS: MathematicssymbolsCalabi–Yau manifoldSettore MAT/03 - GeometriaAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryMAT/03 - GEOMETRIAMathematicsRendiconti Lincei - Matematica e Applicazioni
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