The motivic polynomiality conjecture for cusp punctual quotient schemes

Let (X,p)(X,p) be the cusp singularity x2=y3x^2=y^3, and let Quotd,n(X,p)\operatorname{Quot}_{d,n}(X,p) be its punctual quotient scheme. The motivic polynomiality conjecture. The motive of Quotd,n(X,p)\operatorname{Quot}_{d,n}(X,p) is a polynomial in L\mathbb{L}.

This is a weaker consequence of the exact cusp formula conjecture: it predicts polynomial motives without specifying the coefficients. It would in particular imply that the corresponding punctual quotient schemes admit motivic classes expressed polynomially in the Lefschetz class.

Sources & referencesView supporting material

Primary source

Yifeng Huang and Ruofan Jiang, “Punctual Quot schemes and Cohen–Lenstra series of the cusp singularity”, arXiv:2305.06411 (2023).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.