Verra fourfolds have a distinct small quantum cohomology ring implying they are never birational to very general cubic or Gushel-Mukai fourfolds, with primitive cohomology matching a K3 surface when birational.
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Quantum cohomology and birational geometry of Verra fourfolds
Verra fourfolds have a distinct small quantum cohomology ring implying they are never birational to very general cubic or Gushel-Mukai fourfolds, with primitive cohomology matching a K3 surface when birational.