Mathematics – Algebraic Geometry

Scientific paper

[
0.00
] – not rated yet
Voters
0
Comments 0

1999-08-03

J. Pure and Appl. Algebra, 158, 24 April 2001 pp. 347-366

Mathematics

Algebraic Geometry

18 pages, 3 eps figure, uses epsf.sty. Dedicated to the memory of Gian-Carlo Rota

Scientific paper

The maximal minors of a p by (m + p) matrix of univariate polynomials of degree n with indeterminate coefficients are themselves polynomials of degree np. The subalgebra generated by their coefficients is the coordinate ring of the quantum Grassmannian, a singular compactification of the space of rational curves of degree np in the Grassmannian of p-planes in (m + p)-space. These subalgebra generators are shown to form a sagbi basis. The resulting flat deformation from the quantum Grassmannian to a toric variety gives a new `Gr\"obner basis style' proof of the Ravi-Rosenthal-Wang formulas in quantum Schubert calculus. The coordinate ring of the quantum Grassmannian is an algebra with straightening law, which is normal, Cohen-Macaulay, Gorenstein and Koszul, and the ideal of quantum Pl\"ucker relations has a quadratic Gr\"obner basis. This holds more generally for skew quantum Schubert varieties. These results are well-known for the classical Schubert varieties (n=0). We also show that the row-consecutive p by p-minors of a generic matrix form a sagbi basis and we give a quadratic Gr\"obner basis for their algebraic relations.

**Sottile Frank**

Mathematics – Algebraic Geometry

Scientist

**Sturmfels Bernd**

Mathematics – Commutative Algebra

Scientist

No associations

LandOfFree

If you have personal experience with

A sagbi basis for the quantum Grassmanniandoes not yet have a rating. At this time, there are no reviews or comments for this scientific paper.A sagbi basis for the quantum Grassmannian, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A sagbi basis for the quantum Grassmannian will most certainly appreciate the feedback.

Profile ID: LFWR-SCP-O-374066

Use Google custom search:

All data on this website is collected from public sources.
Our data reflects the most accurate information available at the time of publication.