Automorphisms of prime order of smooth cubic n-folds

Details Automorphisms of prime order of smooth cubic n-folds Automorphisms of prime order of smooth cubic n-folds

2010-02-22

arxiv.org/abs/1002.4136v2

Arch. Math. 97 (2011), 25-37

Mathematics

Algebraic Geometry

10 pages

Scientific paper

10.1007/s00013-011-0247-0

In this paper we give an effective criterion as to when a prime number p is the order of an automorphism of a smooth cubic hypersurface of P^{n+1}, for a fixed n > 1. We also provide a computational method to classify all such hypersurfaces that admit an automorphism of prime order p. In particular, we show that p<2^{n+1} and that any such hypersurface admitting an automorphism of order p>2^n is isomorphic to the Klein n-fold. We apply our method to compute exhaustive lists of automorphism of prime order of smooth cubic threefolds and fourfolds. Finally, we provide an application to the moduli space of principally polarized abelian varieties.

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