Unboundedness of fixed point multiplicities on a K3 surface

Fuente: arXiv
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Main Authors: Hashimoto, Kenji, Takada, Yuta
Format: Preprint
Published: 2025
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author Hashimoto, Kenji
Takada, Yuta
author_facet Hashimoto, Kenji
Takada, Yuta
contents We exhibit automorphisms of a certain K3 surface in $\mathbb{P}^1\times \mathbb{P}^1 \times \mathbb{P}^1$ with an isolated fixed point at which the induced action on the stalk of the structure sheaf is arbitrarily close to the identity. This implies that the multiplicities of these automorphisms at the fixed point can be arbitrarily large. As another application, we show that the intersection multiplicity of two isomorphic curves at a point can be arbitrarily large on this K3 surface.
format Preprint
id arxiv_https___arxiv_org_abs_2508_18814
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Unboundedness of fixed point multiplicities on a K3 surface
Hashimoto, Kenji
Takada, Yuta
Algebraic Geometry
14J28 (Primary), 14J50 (Secondary)
We exhibit automorphisms of a certain K3 surface in $\mathbb{P}^1\times \mathbb{P}^1 \times \mathbb{P}^1$ with an isolated fixed point at which the induced action on the stalk of the structure sheaf is arbitrarily close to the identity. This implies that the multiplicities of these automorphisms at the fixed point can be arbitrarily large. As another application, we show that the intersection multiplicity of two isomorphic curves at a point can be arbitrarily large on this K3 surface.
title Unboundedness of fixed point multiplicities on a K3 surface
topic Algebraic Geometry
14J28 (Primary), 14J50 (Secondary)
url https://arxiv.org/abs/2508.18814