6 papers
The finite degree formula for normalized volumes
Zhiyu Liu
Let be a finite surjective morphism between klt singularities such that . We show that the normal…
Stability conditions and moduli spaces on projective families
Chunyi Li, Zhiyu Liu, Ziqi Liu +4
We extend the construction of stability conditions on projective schemes over a field to projective families over an arbitrary base, and prove that they admit proper relative modul…
Tilt-stability on singular schemes and Bogomolov-Gieseker-type inequalities
Zhiyu Liu, Tianle Mao
We generalize the framework of tilt-stability to singular schemes and formulate the generalized Bogomolov-Gieseker inequality conjecture of Bayer-Macrì-Toda for singular threefolds…
Double EPW cubes from twisted cubics on Gushel-Mukai fourfolds
Soheyla Feyzbakhsh, Hanfei Guo, Zhiyu Liu +1
In this paper, we conduct the first systematic investigation of twisted cubics on Gushel-Mukai (GM) fourfolds. We then study the double EPW cube, a 6-dimensional hyperkähler manifo…
Irreducible symplectic varieties with a large second Betti number
Yuchen Liu, Zhiyu Liu, Chenyang Xu
We prove a general result on the existence of irreducible symplectic compactifications of non-compact Lagrangian fibrations. As an application, we show that the relative Jacobian f…
Atomic sheaves on hyper-Kähler manifolds via Bridgeland moduli spaces
Hanfei Guo, Zhiyu Liu
In this paper, we provide new examples of 1-obstructed and atomic sheaves on an infinite series of locally complete families of projective hyper-Kähler manifolds. More precisely, (…