Degeneration of K3 surfaces with non-symplectic automorphisms

Abstract

We prove that a K3 surface with an automorphism acting on the global $2$-forms by a primitive $m$-th root of unity, $m\ne 1,2,3,4,6$, does not degenerate (assuming the existence of the so-called Kulikov models). A key result used to prove this is the rationality of the actions of automorphisms on the graded quotients of the weight filtration of the $l$-adic cohomology groups of the surface.

v2: 15 pages, a section on compactification of moduli spaces added, presentation improved / v3: 16 pages, minor changes / v4: 15 pages, accepted version

References in corpus (1)

• Semistable Minimal Models of Threefolds in Positive or Mixed Characteristic

Cited by in corpus (1)

• Index of coregularity zero log Calabi-Yau pairs