On some quiver determinantal varieties
Copyright policy )On some quiver determinantal varieties
We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman's complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when the complex resolves a maximal Cohen-Macaulay module supported on the quiver determinantal variety. This allows us to find the set-theoretical defining equations of these varieties. When the variety has codimension one, the only irreducible polynomial function is a relative tensor invariant. As a by-product, we find some vanishing condition for the Kronecker coefficients. In the end, we make a generalization from the quiver setting to the tensor setting.
17 pages. V2. Final version to appear in J. Algebra 2015
- University of California, Riverside United States
determinantal variety, free resolution, Primary 13D02, 14M12, Secondary 16G20, 20C30, Determinantal varieties, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Syzygies, resolutions, complexes and commutative rings, quiver representation, Cohen-Macaulay module, Mathematics - Algebraic Geometry, Kronecker coefficient, FOS: Mathematics, Representations of quivers and partially ordered sets, Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory
determinantal variety, free resolution, Primary 13D02, 14M12, Secondary 16G20, 20C30, Determinantal varieties, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Syzygies, resolutions, complexes and commutative rings, quiver representation, Cohen-Macaulay module, Mathematics - Algebraic Geometry, Kronecker coefficient, FOS: Mathematics, Representations of quivers and partially ordered sets, Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory
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