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Separation of periods of quartic surfaces


The periods of a quartic surface X are complex numbers obtained by integrating a holomorphic 2-form over 2-cycles in X. For any quartic X defined over the algebraic numbers and any 2-cycle G in X, we give a computable positive number c(G) such that the associated period A satisfies either |A| > c(G) or A = 0. This makes it possible in principle to certify a part of the numerical computation of the Picard group of quartics and to study the Diophantine properties of periods of quartics.
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Dates and versions

hal-03022612 , version 1 (24-11-2020)
hal-03022612 , version 2 (01-12-2020)


  • HAL Id : hal-03022612 , version 2


Pierre Lairez, Emre Can Sertöz. Separation of periods of quartic surfaces. 2020. ⟨hal-03022612v2⟩
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