Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: An introduction to Standard Monomial Theory

Seminar | October 29 | 3:45-4:45 p.m. | 939 Evans Hall

 Venkatraman Lakshmibai, Northeastern University

 Department of Mathematics

I shall first introduce the celebrated Grassmannian variety and its canonical projective variety structure under the Plùcker embedding. Then I shall describe a basis for the homogeneous co-ordinate ring of the Grassmannian for the Plùcker embedding in terms of certain monomials in the Plùcker co-ordinates, the so called “Standard Monomials”. I shall then introduce the SCHUBERT subvarities in the Grassmannian and describe a corresponding basis for the for the homogeneous co-ordinate ring of a Schubert subvariety. Time permitting, I shall show some important geometric consequences such as the arithmetic normality & arithmetic Cohen-Macaulayness for the Schubert varieties for the Plùcker embedding.