ALF gravitational instantons and collapsing Ricci-flat metrics on the K3 surface
Location: MSRI: Simons Auditorium
algebraic geometry and GAGA
complex differential geometry
The Kummer construction of Kähler Ricci-flat metrics on the K3 surface provides the prototypical example of the formation of orbifold singularities in non-collapsing sequences of Einstein 4-manifolds. Much less is known about the structure of the singularities forming along sequences of collapsing Einstein metrics. I will describe the construction of large families of Ricci-flat metrics on the K3 surface collapsing to the quotient of a flat 3-torus by an involution. The collapse occurs with bounded curvature away from finitely many points. The geometry around these points is modelled by ALF gravitational instantons
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