By V. Lakshmibai, Justin Brown

This publication provides a entire therapy of the Grassmannian kinds and their Schubert subvarieties, concentrating on the geometric and representation-theoretic facets of Grassmannian forms. study of Grassmannian kinds is based on the crossroads of commutative algebra, algebraic geometry, illustration concept, and combinatorics. for this reason, this article uniquely offers an exhilarating enjoying box for graduate scholars and researchers in arithmetic, physics, and laptop technological know-how, to extend their wisdom within the box of algebraic geometry. the normal monomial concept (SMT) for the Grassmannian kinds and their Schubert subvarieties are brought and the textual content provides a few very important purposes of SMT together with the Cohen–Macaulay estate, normality, targeted factoriality, Gorenstein estate, singular loci of Schubert forms, toric degenerations of Schubert kinds, and the connection among Schubert kinds and classical invariant theory.

This textual content might serve good as a reference ebook for a graduate paintings on Grassmannian kinds and will be a very good supplementary textual content for numerous classes together with these in geometry of round kinds, Schubert types, complicated themes in geometric and differential topology, illustration conception of compact and reductive teams, Lie conception, toric forms, geometric illustration idea, and singularity idea. The reader must have a few familiarity with commutative algebra and algebraic geometry.