arXiv subjects

Carl Mazzanti

Publications and source records attributed to Carl Mazzanti.

2 recordsLinked to original sources

arXiv2026

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.

math.AG↗

arXiv2026

On the Chow ring of double EPW quartics

Double EPW quartics are hyperkähler varieties of dimension 4, first introduced by Iliev, Kapustka, Kapustka, and Ranestad. The general double EPW quartic is isomorphic to a moduli space of twisted sheaves on a $K3$ surface. They have a rich geometry: they are equipped with an anti-symplectic involution and are related to conics in Verra fourfolds in the same way Fano varieties of lines on cubic fourfolds are related to cubic fourfolds themselves. In this work, we exploit this geometry to establish general conjectures about algebraic cycles on hyperkähler varieties in the case of double EPW quartics.

math.AG↗