An update on semisimple quantum cohomology and F-manifolds
| dc.creator | Hertling, C. | |
| dc.creator | Manin, Yu. | |
| dc.creator | Teleman, C. | |
| dc.date | 2008-03-19 | |
| dc.date.accessioned | 2026-07-07T09:27:30Z | |
| dc.date.available | 2026-07-07T09:27:30Z | |
| dc.description | In the first section of this note we show that the Theorem 1.8.1 of Bayer--Manin ([BaMa]) can be strengthened in the following way: {\it if the even quantum cohomology of a projective algebraic manifold $V$ is generically semi--simple, then $V$ has no odd cohomology and is of Hodge--Tate type.} In particular, this addressess a question in [Ci]. In the second section, we prove that {\it an analytic (or formal) supermanifold $M$ with a given supercommutative associative $\Cal{O}_M$--bilinear multiplication on its tangent sheaf $\Cal{T}_M$ is an $F$--manifold in the sense of [HeMa], iff its spectral cover as an analytic subspace of the cotangent bundle $T^*_M$ is coisotropic of maximal dimension.} This answers a question of V. Ginzburg. Finally, we discuss these results in the context of mirror symmetry and Landau--Ginzburg models for Fano varieties. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0803.2769 | |
| dc.identifier | http://arxiv.org/abs/0803.2769 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157127 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 18D50 | |
| dc.title | An update on semisimple quantum cohomology and F-manifolds | |
| dc.type | text |