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BLOWN-UP BOUNDARIES ASSOCIATED WITH AMPLE CONES OF K3 SURFACES

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  23 September 2025

TAIKI TAKATSU Open the ORCID record for TAIKI TAKATSU [Opens in a new window]
TAIKI TAKATSU*
Affiliation:
Department of Mathematics Tokyo University of Science https://ror.org/05sj3n476 2641 Yamazaki, Noda Chiba 278-8510 Japan
*
taiki_takatsu@rs.tus.ac.jp
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Abstract

In this article, we apply the Bestvina–Mess type formula for relatively hyperbolic groups, which is established by Tomohiro Fukaya, to automorphism groups of K3 surfaces, and we show that the virtual cohomological dimension of automorphism groups of K3 surfaces is determined by the covering dimension of the blown-up boundaries associated with their ample cones.

Keywords

K3 surfacesautomorphism group of K3 surfacescohomological dimensionblown-up boundaries of ample conessphere packings

MSC classification

Primary: 14J28: $K3$ surfaces and Enriques surfaces 14J50: Automorphisms of surfaces and higher-dimensional varieties 14J27: Elliptic surfaces

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Type
Article
Information
Nagoya Mathematical Journal , First View , pp. 1 - 30
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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