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.
[BMP26] Vladimiro Benedetti, Laurent Manivel, and Nicolas Perrin
2 Pith papers cite this work. Polarity classification is still indexing.
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A very general complex symmetric Verra fourfold is not Z/2-birational to P^4.
citing papers explorer
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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.
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Equivariant irrationality of very general symmetric Verra fourfolds
A very general complex symmetric Verra fourfold is not Z/2-birational to P^4.