Can We Lift a Family of K3 over a Proper Curve?
نویسنده
چکیده
In this draft, we study the deformation of a proper smooth curve in positive characteristics within the moduli of K3. We expect that the curve can be lifted to the Witt ring with generic fiber a Shimura curve. Given an algebraic closed field k, a double-point K3 surface over k is a projective surface with at worst rational double point singularities whose minimal resolution is a (smooth) K3 surface over k. Let π : X −→ C −→ F̄p be a primitively polarized family of doublepoint K3 surfaces and W = W (F̄p). There exists a ramified Galois covering S −→ C, a family of (smooth) K3 surfaces Y −→ S over S which is a simultaneous resolution of X :
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