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arXiv · 1103.0762

Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes

Benjamin P. Mirabelli·Maksim Maydanskiy
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Abstract

The degree zero part of the quantum cohomology algebra of a smooth Fano toric symplectic manifold is determined by the superpotential function, W, of its moment polytope. In particular, this algebra is semisimple, i.e. splits as a product of fields, if and only if all the critical points of W are non-degenerate. In this paper we prove that this non-degeneracy holds for all smooth Fano toric varieties with facet-symmetric duals to moment polytopes.

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Benjamin P. Mirabelli, Maksim Maydanskiy. 2012-11-12. Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes. https://doi.org/10.3934/era.2011.18.131

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