2022/12/05 by Luc Pirio, Pirio, Luc
Mathematics · #14C21. 53A60 #33E20 #39B32. 14J26 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2212.02556
openalex publication_date 2022/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For d ranging from 2 to 6, we prove that the web by conics naturally defined on any smooth del Pezzo surface of degree d carries an interesting functional identity whose components all are a certain antisymmetric hyperlogarithm of weight 7-d. Our approach is uniform with respect to d and at the end relies on classical results about the action of Weyl groups on the set of lines contained in the considered del Pezzo surface. This series of `del Pezzo's hyperlogarithmic functional identities' is a natural generalization of the famous and well-know 3-term and 5-term identities of the logarithm and dilogarithm ('Abel's relation') which correspond to the cases when d=6 and d=5 respectively. This text ends with a section containing several questions and some possibly interesting perspectives.