Supersingular K3 Surfaces are Unirational

Abstract

We show that supersingular K3 surfaces in characteristic $p\ge 5$ 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 $\rho \ge 19$ in positive characteristic.

due to a mistake in Proposition 3.5, the unirationality of supersingular K3 surfaces remains a conjecture: see the appendix for erratum

References in corpus (3)

• Neron-Severi group preserving lifting of K3 surfaces and applications
• Self Rational Maps of K3 Surfaces
• On the unirationality of supersingular K3 surfaces

Cited by in corpus (5)

• Neron-Severi group preserving lifting of K3 surfaces and applications
• Elliptic fibrations on K3 surfaces and Salem numbers of maximal degree
• On the unirationality of supersingular K3 surfaces
• Curves and cycles on K3 surfaces
• Finite-dimensionality and cycles on powers of K3 surfaces