Motivic and quantum invariance under stratified Mukai flops

TL;DR

This paper investigates the invariance of motivic and quantum properties under stratified Mukai flops, revealing that while Chow motives are preserved, cup products are not, and quantum corrections are identified for specific cases.

Contribution

It demonstrates that fiber products induce isomorphisms on Chow motives for certain stratified Mukai flops and introduces quantum corrections for specific flop types.

Findings

Chow motives are preserved under stratified Mukai flops.

Cup product is generally not preserved in these flops.

Quantum corrections are identified for A_{n, 2}, D_5, and E_{6, I} 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.