Standard monomial bases, moduli of vector bundles, and invariant theory

Simple item page
dc.creatorLakshmibai, V.
dc.creatorRaghavan, K. N.
dc.creatorSankaran, P.
dc.creatorShukla, P.
dc.date2006-04-13
dc.date.accessioned2026-07-07T07:10:54Z
dc.date.available2026-07-07T07:10:54Z
dc.descriptionConsider the diagonal action of the special orthogonal group on the direct sum of a finite number of copies of the standard representation--the underlying field is assumed to be algebraically closed and of characteristic not equal to two. We construct a "standard monomial" basis for the ring of polynomial invariants for this action. We then deduce, by a deformation argument, our main result that this ring of polynomial invariants is Cohen-Macaulay. We give three applications of this result: (1) the first and second fundamental theorems of invariant theory for the above action; (2) Cohen-Macaulayness of the moduli space of equivalence classes of semi-stable vector bundles of rank two and degree zero on a smooth projective curve of genus at least three (for this application, characteristic three is also excluded); (3) a basis in terms of traces for the ring of polynomial invariants for the diagonal adjoint action of the special linear group SL(2) on a finite number of copies of its Lie algebra sl(2).
dc.descriptionlatex; 35 pages
dc.identifierhttps://arxiv.org/abs/math/0604321
dc.identifierhttp://arxiv.org/abs/math/0604321
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111567
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject14M15, 13F50
dc.titleStandard monomial bases, moduli of vector bundles, and invariant theory
dc.typetext

Files

Collections

arXiv