Concavity, Abel transform and the Abel-inverse theorem in smooth complete toric varieties

Martin Weimann (1)

1 UNICAEN - Université de Caen Normandie

We extend the usual projective Abel-Radon transform to the larger context of a smooth complete toric variety X. We define and study toric E-concavity attached to a split vector bundle on X. Then we obtain a multidimensional residual representation of the toric Abel-transform and we prove a toric version of the classical Abel-inverse theorem.

Domains: Mathematics [math]; Mathematics [math]; Algebraic Geometry [math.AG]; Mathematics [math]; Complex Variables [math.CV]

Martin Weimann. Concavity, Abel transform and the Abel-inverse theorem in smooth complete toric varieties. Collectanea Mathematica, 2013, 64 (1), pp.111-133. ⟨10.1007/s13348-011-0050-z⟩. ⟨hal-02137321⟩