Vol. 2, No. 7, 2008

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editors' Interests Submission Guidelines Submission Form Editorial Login 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
Abstract

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.

Keywords
algebra with straightening law, quasimap, Lagrangian Grassmannian, quantum cohomology
Mathematical Subject Classification 2000
Primary: 13F50
Secondary: 13P10, 14N35, 14N15