ALF gravitational instantons and collapsing Ricci-flat metrics on the K3 surface
Kähler Geometry, Einstein Metrics, and Generalizations March 21, 2016 - March 25, 2016
Location: SLMath: Eisenbud Auditorium
algebraic geometry and GAGA
mathematical physics
complex differential geometry
Kahler metric
Ricci flatness
4-manifolds
gravitational instantons
51D25 - Lattices of subspaces and geometric closure systems [See also 05B35]
51E14 - Finite partial geometries (general), nets, partial spreads
14K22 - Complex multiplication and abelian varieties [See also 11G15]
14K20 - Analytic theory of abelian varieties; abelian integrals and differentials
14K10 - Algebraic moduli of abelian varieties, classification [See also 11G15]
14J50 - Automorphisms of surfaces and higher-dimensional varieties
14K15 - Arithmetic ground fields for abelian varieties [See also 11Dxx, 11Fxx, 11G10, 14Gxx]
14472
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
14472
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