Conjecture on the least-degree relations among tautological generators of the moduli space of one-dimensional sheaves

Let $M_{d,\chi}$ be the moduli space under consideration, and let the tautological generators in $A^*(M_{d,\chi})$ be those defined in. A relation among these generators has degree measured in the Chow ring $A^*(M_{d,\chi})$. Least-degree relation conjecture. The relations of least degree among the tautological generators in $A^*(M_{d,\chi})$ occur in $A^d(M_{d,\chi})$. In particular, there is no relation in degree $d-1$. This conjecture is motivated by the numerical data for $4\leq d\leq 9$ and $\chi=1$; it predicts the first degree in which the freeness of the tautological generators fails, while the general assertion remains open.