Forgetful maps between Deligne-Mostow ball quotients

Martin Deraux (1)

1 IF - Institut Fourier

We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P^1, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livné fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also include a retraction of a 3-dimensional ball quotient onto one of its 1-dimensional totally geodesic complex submanifolds.

Domaines: Géométrie différentielle [math.DG]

Martin Deraux. Forgetful maps between Deligne-Mostow ball quotients. Geometriae Dedicata, 2011, 150, pp.377-389. ⟨10.1007/s10711-010-9511-x⟩. ⟨hal-00341618v2⟩