Semisimple quantum cohomology of some Fano varieties

Abstract

We give sufficient conditions for the semisimplicity of quantum cohomology of Fano varieties of Picard rank 1. We apply these techniques to prove new semisimplicity results for some Fano varieties of Picard rank 1 and large index. We also give examples of Fano varieties having a non semisimple small quantum cohomology but a semisimple big quantum cohomology.

27 pages

References in corpus (3)

• Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries
• Small codimension smooth subvarieties in even-dimensional homogeneous spaces with Picard group $\mathbb{Z}$
• Small codimension subvarieties in homogeneous spaces