32 citations · 157 across the 30 of their papers we have counts for
9 papers · 1 filter
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…
A bound on the second Betti number of hyperkähler manifolds of complex dimension six
Justin Sawon
Let M be an irreducible compact hyperkähler manifold of complex dimension six. Under an assumption on the Looijenga-Lunts-Verbitsky decomposition of the cohomology of M, we prove t…
Generalized twistor spaces for hyperkähler manifolds
Rebecca Glover, Justin Sawon
Let M be a hyperkähler manifold. The S^2-family of complex structures compatible with the hyperkähler metric can be assembled into a single complex structure on Z=MxS^2; the result…
Fourier-Mukai transforms, mirror symmetry, and generalized K3 surfaces
Justin Sawon
We study generalized complex structures on K3 surfaces, in the sense of Hitchin. For each real parameter t between one and infinity we exhibit two families of generalized K3 surfac…
Hyperkähler manifolds with circle actions and the Gibbons-Hawking Ansatz
Mustafa Kalafat, Justin Sawon
We show that a complete simply-connected hyperkaehler 4-manifold with an isometric triholomorphic circle action is obtained from the Gibbons-Hawking ansatz with some suitable harmo…
Rozansky-Witten invariants of hyperkähler manifolds
Justin Sawon
We investigate invariants of compact hyperk{ä}hler manifolds introduced by Rozansky and Witten: they associate an invariant to each graph homology class. It is obtained by using th…