Degeneration of K3 surfaces with non-symplectic automorphisms

Yuya Matsumoto

doi:10.4171/RSMUP/123

Degeneration of K3 surfaces with non-symplectic automorphisms

Algebraic Geometry 2023-12-27 v4 Number Theory

Authors: Yuya Matsumoto

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We prove that a K3 surface with an automorphism acting on the global $2$ -forms by a primitive $m$ -th root of unity, $m \neq 1,2,3,4,6$ , 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.

Keywords

K3 surface non-symplectic automorphism degeneration Kulikov model weight filtration l-adic cohomology

Cite

@article{arxiv.1612.07569,
  title  = {Degeneration of K3 surfaces with non-symplectic automorphisms},
  author = {Yuya Matsumoto},
  journal= {arXiv preprint arXiv:1612.07569},
  year   = {2023}
}

Comments

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

Degeneration of K3 surfaces with non-symplectic automorphisms

Abstract

Keywords

Cite

Comments

Related papers