Thomas Zink - Grothendieck-Messing deformation theory for Hyper-Kähler manifolds




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Published on Oct 7, 2014

This is joint work with Andreas Langer. Let 𝑅 be an artinian local ring
with perfect residue class field 𝑘. We define Hyper-Kähler manifolds 𝑋 and
their Beauville-Bogomolov form over 𝑅. We give a lifting criterion in the spirit
of Grothendieck and Messing. Over the small Witt ring 𝑊̂ (𝑅) we associate a
2-display to 𝑋. If 𝑋 is ordinary and 𝑆 → 𝑅 is a surjection of artinian local rings
we show that lifting 𝑋 to 𝑆 is the same as lifting the 2-display of 𝑋.

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