6533b855fe1ef96bd12afd6c
RESEARCH PRODUCT
A construction of equivariant bundles on the space of symmetric forms
Paolo LellaDaniele FaenziAda Boralevisubject
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 spacedescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-11-01 | Revista Matemática Iberoamericana |