The arbitrary-weights character conjecture for homogeneous components of sheaf moduli spaces
Let w‾∈Zr{\overline w}\in{\mathbb Z}^rw∈Zr, let α,β≥1\alpha,\beta\geq 1α,β≥1 satisfy 0≤wi<α+β0\leq w_i<\alpha+\beta0≤wi<α+β and gcd(α,β)=1\gcd(\alpha,\beta)=1gcd(α,β)=1, and let ai=♯{j∣wj=i}a_i=\sharp\{j\mid w_j=i\}ai=♯{j∣wj=i}. Let α′\alpha'α′ be the…