Quantum cohomology via D-modules
| dc.creator | Guest, Martin A. | |
| dc.date | 2002-06-20 | |
| dc.date | 2004-10-06 | |
| dc.date.accessioned | 2026-07-07T04:49:15Z | |
| dc.date.available | 2026-07-07T04:49:15Z | |
| dc.description | We propose a new point of view on quantum cohomology, strongly motivated by the work of Givental and Dubrovin, but closer to differential geometry than the existing approaches. The central object is the D-module which "quantizes" a commutative algebra associated to the (uncompactified) space of rational curves. A standard loop group factorization procedure converts the D-module to Givental's D-module and the commutative algebra to the quantum cohomology algebra. We apply this only to the small quantum cohomology of full flag manifolds and semi-positive toric manifolds, but even in these cases the method is effective. In particular it gives an algorithm (requiring construction of a Groebner basis and solution of a system of o.d.e.) for the quantum product. | |
| dc.description | 21 pages, AMS-TeX. Revised version with many minor corrections and clarifications. Material on flag manifolds has been removed and will appear, in expanded form, in a joint paper with A. Amarzaya | |
| dc.identifier | https://arxiv.org/abs/math/0206212 | |
| dc.identifier | http://arxiv.org/abs/math/0206212 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64352 | |
| dc.subject | Differential Geometry | |
| dc.subject | Quantum Algebra | |
| dc.subject | 14N35, 53D45 | |
| dc.title | Quantum cohomology via D-modules | |
| dc.type | text |