Secondary Chow Invariants beyond Lawson--Massey Products

Source abstract

We construct secondary Chow invariants that cannot be recovered from Lawson--Massey realization. For every smooth complex projective curve $C$ of positive genus and every $n\ge2$, explicit cubical defining systems yield $n$ distinct Massey values in $\rm{CH}^{3}(C\times P^{2},1)$, with zero full indeterminacy, forming a cyclic group of order $n$. All corresponding triples have identical morphic classes and zero morphic, Lawson, and singular Massey brackets, despite nonzero target groups. The values are detected by the Weil pairing. We further construct secondary quotient classes of every finite order on smooth projective varieties with ample canonical bundle in every dimension at least two, and prove that generically finite pullbacks of coprime degree preserve their exact orders. These constructions obstruct integral and prime-local motivic formality, although the corresponding brackets become $\{0\}$ after reduction modulo every integer $m\ge2$. All specified values are torsion and vanish after rationalization.