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On a Torelli Principle for automorphisms of Klein hypersurfaces

V\'ictor Gonz\'alez-AguileraAlvaro LiendoPedro MonteroRoberto Villaflor Loyola
Dec 2022
摘要
We compute all the remaining automorphism groups of Klein hypersurfaces ofdimension n>0 and degree d>2 with (n,d) different from (2,4). We introduce theconcept of extremal polarized Hodge structures, which are structures that admitan automorphism of large prime order. Using this notion, we compute theautomorphism group of the rational polarized Hodge structure of certain Kleinhypersurfaces that we call of Wagstaff type, which are characterized by theexistence of an automorphism of large prime order. For cubic hypersurfaces andsome other values of (n,d), we show that both groups coincide (up toinvolution) as predicted by the Torelli Principle.
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