|
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 264, Pages 69–76
(Mi tm804)
|
|
|
|
This article is cited in 24 scientific papers (total in 24 papers)
An Update on Semisimple Quantum Cohomology and $F$-Manifolds
C. Hertlinga, Yu. I. Maninbc, C. Telemande a Institut für Mathematik, Universität Mannheim, Mannheim, Germany
b Max-Planck-Institut für Mathematik, Bonn, Germany
c Northwestern University, Evanston, USA
d University of Edinburgh, UK
e University of California, Berkeley, USA
Abstract:
In the first section of this note, we show that Theorem 1.8.1 of Bayer–Manin can be strengthened in the following way: If the even quantum cohomology of a projective algebraic manifold $V$ is generically semisimple, then $V$ has no odd cohomology and is of Hodge–Tate type. In particular, this answers a question discussed by G. Ciolli. In the second section, we prove that an analytic (or formal) supermanifold $M$ with a given supercommutative associative $\mathcal O_M$-bilinear multiplication on its tangent sheaf $\mathcal T_M$ is an $F$-manifold in the sense of Hertling–Manin if and only if 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.
Received in July 2008
Citation:
C. Hertling, Yu. I. Manin, C. Teleman, “An Update on Semisimple Quantum Cohomology and $F$-Manifolds”, Multidimensional algebraic geometry, Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 264, MAIK Nauka/Interperiodica, Moscow, 2009, 69–76; Proc. Steklov Inst. Math., 264 (2009), 62–69
Linking options:
https://www.mathnet.ru/eng/tm804 https://www.mathnet.ru/eng/tm/v264/p69
|
Statistics & downloads: |
Abstract page: | 489 | Full-text PDF : | 68 | References: | 89 |
|