Geometry of the Lagrangian Grassmannian Sp(3)/U(3) with applications to Brill-Noether loci

Details Geometry of the Lagrangian Grassmannian Sp(3)/U(3) with applications to Brill-Noether loci Geometry of the Lagrangian Grassmannian Sp(3)/U(3) with applications to Brill-Noether loci

2002-09-13

arxiv.org/abs/math/0209169v2

Mathematics

Algebraic Geometry

45 pages, revision of applications to Brill-Noether loci

Scientific paper

The geometry of Sp(3)/U(3) as a subvariety of Gr(3,6) is explored to explain several examples given by Mukai of non-abelian Brill-Noether loci, and to give some new examples. These examples identify Brill-Noether loci of vector bundles on linear sections of the Lagrangian Grassmannian Sp(3)/U(3) with orthogonal linear sections of the dual variety and vice versa. A main technical result of independent interest is the fact that any nodal hyperplane section of the Lagrangian Grassmannian projected from the node is a linear section of the Grassmannian Gr(2,6).

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