Supersingular K3 Surfaces are Unirational
Abstract
We show that supersingular K3 surfaces in characteristic p≥5 are related sequences of very special correspondences. This is not enough to conclude that they are unirational. As a byproduct, we exhibit a fibration structure on the moduli space of rigidified K3 crystals. We also establish Shioda-Inose type isogeny theorems for K3 surfaces with Picard rank ≥19 in positive characteristic.
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