Family 053Algebraic and complex geometryNo LeanNot yet digested
A counterexample to Pixton completeness in Chow
Constructs a tautological relation on a moduli space of stable pointed curves that vanishes in rational Chow, hence in rational cohomology, but lies outside Pixton's original relation span. This disproves the Chow and rational-cohomological forms of his original completeness conjecture.
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A high-arity counterexample to Pixton completeness in Chow
Sep 24, 2026·paper.pdf
We disprove the Chow and rational-cohomological forms of Pixton's completeness conjecture for his original relation system. We construct a formal tautological class outside the original Pixton relation span whose image is zero in the Chow ring and in rational cohomology. The example has genus and markings.