About the invariants of the family of cubic surfaces: Conversations with Raymond

par Michel Bauer (CEA Saclay)

jeudi 26 mai 2016, 11:00 → 12:00 Europe/Paris

Auditorium (Annecy-le-Vieux)

Cubic curves are popular in theoretical physics due to their connexion with elliptic functions. Cubic surfaces are less well-known but also have a very rich geometry and play some role in physics. In this talk I will describe the interaction I had on this topic in 2014-2015 with Raymond Stora, who was motivated by a classification of families of Born-Infeld actions. I shall describe briefly the classical geometry of cubic surfaces (principally the 27 seven lines and their intersection pattern). Then I'll turn to the polynomial invariants of the family of cubic surfaces, which were at the heart of Raymond's preoccupations. I'll start with an overview of general properties of invariants and discuss some efficient methods to compute their number. I shall rely on simple examples familiar to physicists.