32 citations · 157 across the 30 of their papers we have counts for
31 papers
Birational geometry of Beauville-Mukai systems III: asymptotic behavior
Xuqiang Qin, Justin Sawon
Suppose that a Hilbert scheme of points on a K3 surface S of Picard rank one admits a rational Lagrangian fibration. We show that if the degree of the surface is sufficiently large…
Birational geometry of Beauville-Mukai systems II: general theory in low ranks
Xuqiang Qin, Justin Sawon
Via wall-crossing, we study the birational geometry of Beauville-Mukai systems on K3 surfaces with Picard rank one. We show that there is a class of walls which are always present…
Birational geometry of Beauville-Mukai systems I: the rank three and genus two case
Xuqiang Qin, Justin Sawon
We study wall-crossing for the Beauville-Mukai system of rank three on a general genus two K3 surface. We show that such a system is related to the Hilbert scheme of ten points on…
Topological bounds on hyperkähler manifolds
Justin Sawon
We conjecture that certain curvature invariants of compact hyperkähler manifolds are positive/negative. We prove the conjecture in complex dimension four, give an "experimental pro…
Deformations of compact Prym fibrations to Hitchin systems
Justin Sawon, Chen Shen
We describe certain Lagrangian fibrations by Prym varieties on holomorphic symplectic varieties that deform to compactifications of Sp-Hitchin systems.
Singular fibres of very general Lagrangian fibrations
Justin Sawon
Let be a (holomorphic) Lagrangian fibration that is very general in the moduli space of Lagrangian fibrations. We conjecture that the singular fibres i…