New moduli spaces of pointed curves and pencils of flat connections
| dc.creator | Losev, A. | |
| dc.creator | Manin, Yu. | |
| dc.date | 2000-01-01 | |
| dc.date | 2000-03-20 | |
| dc.date.accessioned | 2026-07-07T04:33:10Z | |
| dc.date.available | 2026-07-07T04:33:10Z | |
| dc.description | It is well known that formal solutions to the Associativity Equations are the same as cyclic algebras over the homology operad $(H_*(\bar{M}_{0,n+1}))$ of the moduli spaces of $n$--pointed stable curves of genus zero. In this paper we establish a similar relationship between the pencils of formal flat connections (or solutions to the Commutativity Equations) and homology of a new series $\bar{L}_n$ of pointed stable curves of genus zero. Whereas $\bar{M}_{0,n+1}$ parametrizes trees of $\bold{P}^1$'s with pairwise distinct nonsingular marked points, $\bar{L}_n$ parametrizes strings of $\bold{P}^1$'s stabilized by marked points of two types. The union of all $\bar{L}_n$'s forms a semigroup rather than operad, and the role of operadic algebras is taken over by the representations of the appropriately twisted homology algebra of this union. | |
| dc.description | 37 pages, AMSTex. Several typos corrected, a reference added, subsection 3.2.2 revised, subsection 3.2.4 added | |
| dc.identifier | https://arxiv.org/abs/math/0001003 | |
| dc.identifier | http://arxiv.org/abs/math/0001003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58473 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | New moduli spaces of pointed curves and pencils of flat connections | |
| dc.type | text |