Birational automorphisms of quartic Hessian surfaces |
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Authors: | Igor Dolgachev JongHae Keum |
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Affiliation: | Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 ; Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-012, Korea |
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Abstract: | We find generators of the group of birational automorphisms of the Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16 which embeds naturally in the even unimodular lattice of rank 26 and signature . The generators are related to reflections with respect to some Leech roots. A similar observation was made first in the case of quartic Kummer surfaces in the work of Kondo. We shall explain how our generators are related to the generators of the group of birational automorphisms of a general quartic Kummer surface which is birationally isomorphic to a special Hessian surface. |
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Keywords: | Quartic Hessian surfaces automorphisms K3 surface Leech lattice |
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