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- W2039731427 abstract "Abstract Let V be an algebraic K3 surface defined over a number field K . Suppose V has Picard number two and an infinite group of automorphisms A = Aut(V/K). In this paper, we introduce the notion of a vector height h : V → Pic( V ) ⊗ and show the existence of a canonical vector height with the following properties: where σ ∈ A, σ * is the pushforward of σ (the pullback of σ −1 ), and h D is a Weil height associated to the divisor D . The bounded function implied by the O(1) does not depend on P . This allows us to attack some arithmetic problems. For example, we show that the number of rational points with bounded logarithmic height in an A-orbit satisfies Here, μ(P) is a nonnegative integer, s is a positive integer, and ω is a real quadratic fundamental unit." @default.
- W2039731427 created "2016-06-24" @default.
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- W2039731427 date "2003-12-01" @default.
- W2039731427 modified "2023-10-01" @default.
- W2039731427 title "Canonical Vector Heights on Algebraic K3 Surfaces with Picard Number Two" @default.
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- W2039731427 doi "https://doi.org/10.4153/cmb-2003-048-x" @default.
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