Motivic and quantum invariance under stratified Mukai flops

Abstract

For stratified Mukai flops of type $A_{n,k},D_{2k+1}$ and $E_{6,I}$, it is shown the fiber product induces isomorphisms on Chow motives. In contrast to (standard) Mukai flops, the cup product is generally not preserved. For $A_{n,2}$, $D_5$ and $E_{6,I}$ flops, quantum corrections are found through degeneration/deformation to ordinary flops.