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  Non-symplectic automorphisms of odd prime order on manifolds of K3[n]-type

Camere, C., & Cattaneo, A. (2020). Non-symplectic automorphisms of odd prime order on manifolds of K3[n]-type. Manuscripta Mathematica, 163(3-4), 299-342. doi:10.1007/s00229-019-01163-4.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0006-9E63-9 Version Permalink: https://hdl.handle.net/21.11116/0000-0007-4DCE-C
Genre: Journal Article
Latex : Non-symplectic automorphisms of odd prime order on manifolds of $K3^{[n]}$-type

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 Creators:
Camere, Chiara, Author
Cattaneo, Alberto1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry
 Abstract: We classify non-symplectic automorphisms of odd prime order on irreducible holomorphic symplectic manifolds which are deformations of Hilbert schemes of any number n of points on K3 surfaces, extending results already known for n=2.
In order to do so, we study the properties of the invariant lattice of the automorphism (and its orthogonal complement) inside the second cohomology lattice of the manifold. We also explain how to construct automorphisms with fixed action on cohomology: in the cases n=3,4 the examples provided allow to realize all admissible actions in our classification. For n=4, we present a construction of non-symplectic automorphisms on the Lehn-Lehn-Sorger-van Straten eightfold, which come from automorphisms of the underlying cubic fourfold.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 1802.00192
URI: http://arxiv.org/abs/1802.00192
DOI: 10.1007/s00229-019-01163-4
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Title: Manuscripta Mathematica
  Abbreviation : Manuscripta Math.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 163 (3-4) Sequence Number: - Start / End Page: 299 - 342 Identifier: -