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Wild automorphisms of varieties with Kodaira dimension 0

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Abstract

An automorphism σ of a projective variety X is said to be wild if σ(Y) ≠ Y for every non-empty subvariety \({Y \subsetneq X}\) . In [1] Z. Reichstein, D. Rogalski, and J.J. Zhang conjectured that if X is an irreducible projective variety admitting a wild automorphism then X is an abelian variety, and proved this conjecture for dim(X) ≤ 2. As a step toward answering this conjecture in higher dimensions we prove a structure theorem for projective varieties of Kodaira dimension 0 admitting wild automorphisms. This essentially reduces the Kodaira dimension 0 case to a study of Calabi-Yau varieties, which we also investigate. In support of this conjecture, we show that there are no wild automorphisms of certain Calabi-Yau varieties.

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  1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195, USA

    Antonio Kirson

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  1. Antonio Kirson
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Correspondence to Antonio Kirson.

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Kirson, A. Wild automorphisms of varieties with Kodaira dimension 0. Ann. Univ. Ferrara 56, 327–333 (2010). https://doi.org/10.1007/s11565-010-0104-2

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  • DOI: https://doi.org/10.1007/s11565-010-0104-2

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