Search results for "Stable vector bundles"

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A construction of equivariant bundles on the space of symmetric forms

2021

We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of stable vector bundles of rank d-1 on P^d, which are moreover equivariant for SL_2(C). The presentation matrix of these bundles attains Westwick's upper bound for the dimension of vector spaces of matrices of constant rank and fixed size.

Pure mathematicsRank (linear algebra)General MathematicsVector bundlestable vector bundlesSpace (mathematics)Mathematics - Algebraic GeometryMatrix (mathematics)symmetric formsDimension (vector space)FOS: MathematicsRepresentation Theory (math.RT)Algebraic Geometry (math.AG)Mathematics::Symplectic Geometryhomogeneous varietyMathematicsequivariant resolution14J60quiver representationconstant rank matrixhomogeneous bundleEquivariant mapgroup actionStable vector bundles; symmetric forms; group action; equivariant resolution; constant rank matrix; homogeneous bundle; homogeneous variety; quiver representationMathematics - Representation TheoryResolution (algebra)Vector spaceRevista Matemática Iberoamericana
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