Search results for " geometria"

showing 10 items of 291 documents

Deformations of Calabi-Yau manifolds in Fano toric varieties

2020

In this article, we investigate deformations of a Calabi-Yau manifold $Z$ in a toric variety $F$, possibly not smooth. In particular, we prove that the forgetful morphism from the Hilbert functor $H^F_Z$ of infinitesimal deformations of $Z$ in $F$ to the functor of infinitesimal deformations of $Z$ is smooth. This implies the smoothness of $H^F_Z $ at the corresponding point in the Hilbert scheme. Moreover, we give some examples and include some computations on the Hodge numbers of Calabi-Yau manifolds in Fano toric varieties.

Pure mathematicsGeneral MathematicsInfinitesimalFano plane01 natural sciencesMathematics - Algebraic GeometryMorphismMathematics::Algebraic GeometryMathematics::Category TheoryFOS: MathematicsCalabi–Yau manifold0101 mathematicsMathematics::Symplectic GeometryAlgebraic Geometry (math.AG)ComputingMethodologies_COMPUTERGRAPHICSMathematicsFunctorComputer Science::Information Retrieval010102 general mathematicsToric varietyFano toric varieties · Calabi-Yau manifolds · Deformations of subvarietiesManifold010101 applied mathematicsHilbert scheme14J32 14J45 32G10Settore MAT/03 - GeometriaMathematics::Differential Geometry
researchProduct

Del Pezzo elliptic varieties of degree d <= 4

2019

Let Y be a smooth del Pezzo variety of dimension n&gt;=3, i.e. a smooth complex projective variety endowed with an ample divisor H such that K_Y = (n+1)H. Let d be the degree H^n of Y and assume that d &gt;= 4. Consider a linear subsystem of |H| whose base locus is zero-dimensional of length d. The subsystem defines a rational map onto P^{n-1} and, under some mild extra hypothesis, the general pseudofibers are elliptic curves. We study the elliptic fibration X -&gt; P^{n-1} obtained by resolving the indeterminacy and call the variety X a del Pezzo elliptic variety. Extending the results of [7] we mainly prove that the Mordell-Weil group of the fibration is finite if and only if the Cox ring…

Pure mathematicsMathematics (miscellaneous)Elliptic fibrationSettore MAT/03 - GeometriaCox ringsDel Pezzo varietyTheoretical Computer ScienceDegree (temperature)Mathematics
researchProduct

Projecting 4-folds from G(1, 5) to G(1, 4)

2002

We study 4-dimensional subvarieties of the Grassmannian G(1,5) with singular locus of dimension at most 1 that can be isomorphically projected to G(1,4).

Pure mathematicsMathematics::Algebraic GeometryNumber theoryGeneral MathematicsGrassmannianGeometryAlgebraic geometrySettore MAT/03 - GeometriaLocus (mathematics)Computer Science::DatabasesMathematicsGrassmannians projections
researchProduct

On cubic elliptic varieties

2013

Let X-&gt;P^(n-1) be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of P^(n+1) from a line L not contained in Y. We prove that the Mordell-Weil group of the elliptic fibration is finite if and only if the Cox ring of X is finitely generated. We also provide a presentation of the Cox ring of X when it is finitely generated.

Pure mathematicsMathematics::Commutative AlgebraGroup (mathematics)Applied MathematicsGeneral MathematicsFibrationMathematics - Algebraic GeometryHypersurfaceMathematics::Algebraic GeometryProjection (mathematics)Line (geometry)14C20 14DxxFOS: MathematicsMathematics (all)Finitely-generated abelian groupSettore MAT/03 - GeometriaCox ringAlgebraic Geometry (math.AG)Mathematics
researchProduct

On the irreducibility of Hurwitz spaces of coverings with two special fibers

2012

Pure mathematicsMonodromyGeneral MathematicsIrreducibilitySettore MAT/03 - GeometriaHurwitz spaces special fibers branched coverings monodromy braid moves.Mathematics
researchProduct

Skeleta of affine hypersurfaces

2014

A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation of its Newton polytope, we provide a purely combinatorial construction of a compact topological space S as a union of components of real dimension n, and prove that S embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S.

Pure mathematicsPolynomialMathematicsofComputing_GENERALAffinePolytopeComplex dimensionTopological spaceTriangulation14J70Mathematics - Algebraic GeometryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsHomotopy equivalenceAlgebraic Topology (math.AT)Mathematics - Algebraic TopologyKato–Nakayama spaceAlgebraic Geometry (math.AG)SkeletonMathematicsToric degenerationTriangulation (topology)HomotopyLog geometry14J70 14R99 55P10 14M25 14T05RetractionHypersurfaceHypersurfaceNewton polytopeSettore MAT/03 - GeometriaGeometry and TopologyAffine transformationKato-Nakayama space14R99
researchProduct

Near abelian profinite groups

2012

Abstract A compact p-group G (p prime) is called near abelian if it contains an abelian normal subgroup A such that G/A has a dense cyclic subgroup and that every closed subgroup of A is normal in G. We relate near abelian groups to a class of compact groups, which are rich in permuting subgroups. A compact group is called quasihamiltonian (or modular) if every pair of compact subgroups commutes setwise. We show that for p ≠ 2 a compact p-group G is near abelian if and only if it is quasihamiltonian. The case p = 2 is discussed separately.

Pure mathematicsProfinite groupApplied MathematicsGeneral Mathematicstopologically quasihamiltonian groupProjective covermodular groupcompact groupsSettore MAT/03 - GeometriaAbelian groupMathematicspro-$p$-group
researchProduct

Locally compact groups which are just not compact

2010

A Just-Non-Compact group, or briefly a JNC group, is a Hausdorff topological group which is not a compact group but all of whose proper Hausdorff quotients are compact groups. Intuitively, it is clear that these groups are rich in compact quotients. Locally compact JNC groups are largely described in the present paper.

Pure mathematicsSettore MAT/02 - AlgebraSettore MAT/05 - Analisi MatematicaGeneral MathematicsJust-Non-Compact groups Lie groups compact groupsLie groupLocally compact spaceSettore MAT/03 - GeometriaMathematics
researchProduct

Cox ring of the generic fiber

2017

Abstract Given a surjective morphism π : X → Y of normal varieties satisfying some regularity hypotheses we prove how to recover a Cox ring of the generic fiber of π from the Cox ring of X. As a corollary we show that in some cases it is also possible to recover the Cox ring of a very general fiber, and finally we give an application in the case of the blowing-up of a toric fiber space.

Pure mathematicsStatistics::TheoryAlgebra and Number TheoryMathematics::Commutative AlgebraFiber (mathematics)Quantitative Biology::Tissues and Organs010102 general mathematics14C20 14Q15 14N25Space (mathematics)01 natural sciencesSurjective functionMathematics - Algebraic GeometryMorphismCorollary0103 physical sciencesFOS: MathematicsFiber spaces010307 mathematical physicsSettore MAT/03 - Geometria0101 mathematicsCox ringCox ringAlgebraic Geometry (math.AG)Mathematics
researchProduct

Big Vector Bundles on Surfaces and Fourfolds

2019

The aim of this note is to exhibit explicit sufficient criteria ensuring bigness of globally generated, rank-$r$ vector bundles, $r \geqslant 2$, on smooth, projective varieties of even dimension $d \leqslant 4$. We also discuss connections of our general criteria to some recent results of other authors, as well as applications to tangent bundles of Fano varieties, to suitable Lazarsfeld-Mukai bundles on four-folds, etcetera.

Pure mathematicsbig vector bundles Lazarsfeld-MukaipositivityGeneral Mathematics010102 general mathematicsDimension (graph theory)Vector bundleTangentFano planevector bundles01 natural sciences14J60 (Primary) 14J35 (Secondary)010101 applied mathematicsMathematics - Algebraic Geometryvector bundles; positivity; vanishing criteriaMathematics::Algebraic Geometryvanishing criteriaFOS: MathematicsSettore MAT/03 - Geometria0101 mathematicsAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryMathematics
researchProduct