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Title:
Burkhardt, Todd, Igusa, Beauville and rational quartic threefolds
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Abstract:
Burkhardt and Igusa quartic threefolds are classically known to be rational. They generate a pencil of quartics that all admit an action of the symmetric group of degree six. Bondal and Prokhorov asked which threefolds in this pencil are rational and which are not. All these threefolds are singular, so Iskovskikh and Manin's result cannot be applied here. Recently Beauiville proved that every quartic threefold in this pencil is irrational
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