Degeneration of K3 surfaces with non-symplectic automorphisms

• DOI: 10.48550/arxiv.1612.07569
• Publication Date: 2023-03-17
• Authors: Matsumoto, Yuya
• Keywords: Mathematics - Algebraic Geometry; Mathematics - Number Theory; FOS: Mathematics; Number Theory (math.NT); 0101 mathematics; Primary 14J28, Secondary 11G25, 14L30, 14D06, 14J50; 01 natural sciences; Algebraic Geometry (math.AG)

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.