Quasimaps, straightening laws, and quantum cohomology for the Lagrangian Grassmannian

Ruffo, James

doi:10.2140/ant.2008.2.819

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Quasimaps, straightening laws, and quantum cohomology for the Lagrangian Grassmannian

James Ruffo

Vol. 2 (2008), No. 7, 819–858

DOI: 10.2140/ant.2008.2.819

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

Milestones

Received: 4 June 2008

Revised: 31 July 2008

Accepted: 12 September 2008

Published: 23 November 2008

Authors

James Ruffo
Department of Mathematics, Science, and Statistics State University of New York - College at Oneonta Oneonta, NY 13820 United States
http://employees.oneonta.edu/ruffojv

Vol. 2, No. 7, 2008