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Article Dans Une Revue Advances in Mathematics Année : 2024

Hyperlogarithmic functional equations on del Pezzo surfaces

Résumé

For any $d\in \{1,\ldots,6\}$, we prove that the web of conics on a del Pezzo surface of degree $d$ carries a functional identity whose components are antisymmetric hyperlogarithms of weight $7-d$. Our approach is uniform with respect to $d$ and relies on classical results about the action of the Weyl group on the set of lines on the del Pezzo surface. These hyperlogarithmic functional identities are natural generalizations of the classical 3-term and (Abel's) 5-term identities satisfied by the logarithm and the dilogarithm, which correspond to the cases when $d=6$ and $d=5$ respectively.
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Dates et versions

hal-04303999 , version 1 (24-11-2023)

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Ana-Maria Castravet, Luc Pirio. Hyperlogarithmic functional equations on del Pezzo surfaces. Advances in Mathematics, 2024, 442, pp.109567. ⟨10.48550/arXiv.2301.06775⟩. ⟨hal-04303999⟩
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