Family 041Algebraic and complex geometryNo LeanNot yet digested
Hyperkähler SYZ and projective-space bases
Proves the strong hyperkähler SYZ conjecture: every holomorphic line bundle with nonzero nef isotropic first Chern class on a compact irreducible holomorphic symplectic Kähler manifold is semiample. It also proves that every projective Lagrangian fibration with normal projective base has projective space as its base, in every dimension and deformation type.
Manuscripts in this family · 2
Projective-space bases of Lagrangian fibrations
Sep 23, 2026·main.pdf
We prove that the normal projective base of a projective Lagrangian fibration from a compact irreducible holomorphic symplectic Kähler manifold is projective space. This resolves the projective-space base conjecture for such fibrations in every dimension and deformation type.
The strong hyperkähler SYZ conjecture
Sep 23, 2026·main.pdf
We prove the strong hyperkähler SYZ conjecture: every holomorphic line bundle with nonzero nef isotropic first Chern class on a compact irreducible holomorphic symplectic Kähler manifold is semiample.