Vol. 2, No. 7, 2008

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Quasimaps, straightening laws, and quantum cohomology for the Lagrangian Grassmannian

James Ruffo

Vol. 2 (2008), No. 7, 819–858

The Drinfel’d Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural projective embedding arising from the canonical embedding of the Lagrangian Grassmannian. We show that the defining ideal of any Schubert subvariety of the Drinfel’d Lagrangian Grassmannian is generated by polynomials which give a straightening law on an ordered set. Consequentially, any such subvariety is Cohen–Macaulay and Koszul. The Hilbert function is computed from the straightening law, leading to a new derivation of certain intersection numbers in the quantum cohomology ring of the Lagrangian Grassmannian.

algebra with straightening law, quasimap, Lagrangian Grassmannian, quantum cohomology
Mathematical Subject Classification 2000
Primary: 13F50
Secondary: 13P10, 14N35, 14N15
Received: 4 June 2008
Revised: 31 July 2008
Accepted: 12 September 2008
Published: 23 November 2008
James Ruffo
Department of Mathematics, Science, and Statistics
State University of New York - College at Oneonta
Oneonta, NY 13820
United States