Abstract
A morphism of smooth varieties of the same dimension is called
real fibered if the inverse image of the real part of the target is the
real part of the source. It goes back to Ahlfors that a real algebraic
curve admits a real fibered morphism to the projective line if and only
if the real part of the curve disconnects its complex part. Inspired by
this result, in a joint work with Mario Kummer and Cédric Le Texier, we
are interested in characterising real algebraic varieties of dimension n
admitting real fibered morphisms to the n-dimensional projective space.
We present a criterion to construct real fibered morphisms that arise as
finite surjective linear projections from an embedded variety; this
criterion relies on topological linking numbers. We address special
attention to real algebraic surfaces. We classify all real fibered
morphisms from real del Pezzo surfaces to the projective plane and
determine when such morphisms arise as the composition of a projective
embedding with a linear projection.