The circle method applies to rational points on Perazzo-type cubic fourfolds and exceeds the square-root barrier.
Salberger, Tamagawa measures on universal torsors and points of bounded height on Fano varieties.Ast´ erisque251(1998), 91–258
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Beyond the square-root barrier: cubic forms of Perazzo type
The circle method applies to rational points on Perazzo-type cubic fourfolds and exceeds the square-root barrier.