# American Institute of Mathematical Sciences

2011, 18: 131-143. doi: 10.3934/era.2011.18.131

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

 1 Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom 2 Yale University, MathematicsDepartment, PO Box 208283, New Haven, Connecticut 06520, United States

Received  March 2011 Revised  July 2011 Published  September 2011

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.
Citation: Maksim Maydanskiy, Benjamin P. Mirabelli. Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes. Electronic Research Announcements, 2011, 18: 131-143. doi: 10.3934/era.2011.18.131
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