Expected number and distribution of critical points of real Lefschetz pencils

Michele Ancona (1)

1 AGL - Algèbre, géométrie, logique

We give an asymptotic probabilistic real Riemann-Hurwitz formula computing the expected real ramification index of a random covering over the Riemann sphere. More generally, we study the asymptotic expected number and distribution of critical points of a random real Lefschetz pencil over a smooth real algebraic variety.

Domaines: Géométrie algébrique [math.AG]; Géométrie différentielle [math.DG]

Michele Ancona. Expected number and distribution of critical points of real Lefschetz pencils. 2018. ⟨hal-01740270⟩