Zero-cycles on Moduli Spaces of Twisted Sheaves and Applications to Double EPW Quartics

Chen, Li, Zhang, and Zhang extended the results of Shen, Yin, and Zhao on zero-cycles on moduli spaces of stable objects on $K3$ surfaces to the twisted setting. In this work, we complement this by extending results by Vial and Martin–Vial to moduli spaces on twisted $K3$ surfaces. Exploiting the fact that double EPW quartics can be realised as moduli spaces of twisted sheaves, we show that effective zero-cycles agree if and only if they agree in the associated Verra fourfold and show that the twisted Beauville–Voisin class of Chen, Li, Zhang, and Zhang agrees with the Beauville–Voisin class in that case.