Search results for " 14C05"

showing 2 items of 2 documents

Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces

2007

This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…

Hilbert manifoldHilbert's basis theoremHilbert matrix01 natural sciencesMathematics - Algebraic Geometrysymbols.namesakeCharacteristic classesPrimary 14C05Secondary 14C170103 physical sciencesFOS: Mathematics[MATH]Mathematics [math]0101 mathematicsAlgebraic Geometry (math.AG)ComputingMilieux_MISCELLANEOUSMathematicsHilbert–Poincaré seriesHilbert's second problemHilbert series and Hilbert polynomialAlgebra and Number Theory010102 general mathematicsHilbert's fourteenth problemUniversal formulasPrimary 14C05; Secondary 14C17Hilbert schemes of pointsAlgebraHilbert schemesymbols[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physics
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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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