We prove the generalized Franchetta conjecture for the locally complete family of hyper-
Kähler eightfolds constructed by Lehn–Lehn–Sorger–van Straten (LLSS). As a corollary, we …

We study the birational geometry of moduli spaces of semistable sheaves on the projective
plane via Bridgeland stability conditions. We show that the entire MMP of their moduli …

For any smooth projective moduli space M of Gieseker stable sheaves on a complex
projective K3 surface (or an abelian surface) S, we prove that the Chow motive h (M) h (M) …

We investigate how the motive of hyper-Kähler varieties is controlled by weight-2 (or surface-
like) motives via tensor operations. In the first part, we study the Voevodsky motive of …

We study the (covering) gonality of abelian varieties and their orbits of zero-cycles for
rational equivalence. We show that any orbit for rational equivalence of zerocycles of degree …

We investigate the Lefschetz standard conjecture for degree 2 cohomology of hyper-Kähler
manifolds admitting a covering by Lagrangian subvarieties. In the case of a Lagrangian …

Moduli spaces of stable objects in the derived category of a-group of the moduli space of
stable objects. We discuss its connection with Voisin's recent proposal via constant cycle …

In this paper, we study Bloch's conjecture for zero cycles on K3 surfaces and hyper-K\" ahler
varieties. We prove Bloch's conjecture for reflexive autoequivalences on K3 surfaces. This …

We explore the connection between K3 categories and 0-cycles on holomorphic symplectic
varieties. In this paper, we focus on Kuznetsov's noncommutative K3 category associated to …

We introduce a new ascending filtration, that we call the co-radical filtration in analogy with
the basic theory of co-algebras, on the Chow groups of pointed smooth projective varieties …