2026/07/14 by Jiarui Fei
Mathematics · #math.AG #math.RT
We study the topological Euler characteristic of the quiver Grassmannian for a generic representation. We give a Chern class formula and a finite torus-localization formula. If the quiver Q is acyclic, the formula can be combined with the covariant calculation of Derksen--Schofield--Weyman to obtain a finite integral linear combination of covariant multiplicities, or equivalently of semi-invariant multiplicities for a single flag-extended quiver of Q. We also give explicit formulas and examples for generalized Kronecker quivers, and record the same construction for multiplicative characteristic genera.