Séminaires : Séminaire d'Algèbre

For any d in {1,…,6}, we prove that the web of conics on a del Pezzo surface of degree d carries a functional identity HLog(7-d) 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 HLog(7-d) are natural generalizations of the classical 3-term and (Abel's) 5-term identities of the logarithm and the dilogarithm, which are the identities HLog(1) and HLog(2) corresponding to the cases d=6 and d=5 respectively.
If time allows, I will give a list of many nice properties enjoyed by the 5-term identity of the dilogarithm and will explain that most of these properties (such as being of cluster type) have natural generalizations which are satisfied by the weight 3 hyperlogarithmic identity HLog(3).
The talk will be mainly based on the preprint arXiv:2301.06775 written with Ana-Maria Castravet.

Exceptionally, this talk will take place in hybrid mode in room 1013 of the Sophie Germain building (8, place Aurélie Nemours, 75013 Paris).