Algebraic orbifold quantum products
| dc.creator | Abramovich, Dan | |
| dc.creator | Graber, Tom | |
| dc.creator | Vistoli, Angelo | |
| dc.date | 2001-12-01 | |
| dc.date.accessioned | 2026-07-07T04:44:55Z | |
| dc.date.available | 2026-07-07T04:44:55Z | |
| dc.description | The purpose of this note is to give an overview of our work on defining algebraic counterparts for W. Chen and Y. Ruan's Gromov-Witten Theory of orbifolds. This work will be described in detail in a subsequent paper. The presentation here is generally based on lectures given by two of us at the Orbifold Workshop in Madison, Wisconsin. Following the spirit of the workshop, we give a nontechnical introduction to stacks, a general discussion of twisted stable maps, and a run-through of the issues that arise when generalizing Gromov-Witten theory to Deligne-Mumford stacks. We make a special effort to make our constructions as canonical as we can, systematically using the language of algebraic stacks. Our efforts bear some concrete fruits; in particular, we are able to define the Chen-Ruan product in degree 0 (the so called stringy cohomology of the stack) with integer coefficients. Beware - this note may be vanishing in front of your eyes: first, a somewhat less technical version intended for the workshop proceedings will shortly (we hope) be submitted. Second, a much more detailed paper is in preparation, in which all the technicalities which are swept under the rug here are discussed, as well as some cool stuff about taking roots. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0112004 | |
| dc.identifier | http://arxiv.org/abs/math/0112004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62788 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14N35; 14A20; 14H10 | |
| dc.title | Algebraic orbifold quantum products | |
| dc.type | text |