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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
References:
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
English version:
Proceedings of the Steklov Institute of Mathematics, 2009, Volume 264, Pages 62–69
DOI: https://doi.org/10.1134/S0081543809010088
Bibliographic databases:
UDC: 514.743.2
Language: English
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
Citation in format AMSBIB
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\by C.~Hertling, Yu.~I.~Manin, C.~Teleman
\paper An Update on Semisimple Quantum Cohomology and $F$-Manifolds
\inbook Multidimensional algebraic geometry
\bookinfo Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences
\serial Trudy Mat. Inst. Steklova
\yr 2009
\vol 264
\pages 69--76
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\yr 2009
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\pages 62--69
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  • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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