From the 2 of 6 linked papers with an AI index.
6 papers
Stability conditions and moduli spaces on projective families
Chunyi Li, Zhiyu Liu, Ziqi Liu +4
The paper extends Bridgeland stability conditions from projective schemes to families over arbitrary bases, establishing proper relative moduli spaces and proving related mass‑Hom…
The finite degree formula for normalized volumes
Zhiyu Liu
The paper proves that for a finite surjective morphism between klt singularities preserving the log canonical divisor, the normalized volume at the source equals the degree of the…
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 threefold…
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,…
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…
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 manif…