On the irrationality of surfaces in three-dimensional projective space (following F. Bastianelli)

The degree of irrationality of an $n$-dimensional complex projective manifold $X$ is the least number $k$ such that there exists a map of degree $k$ from $X$ to the $n$-dimensional projective space. It is known that the degree of irrationality can decrease if a manifold is multiplied by a projective space. This gives a motivation to define a notion of the stable degree of irrationality. In the talk it will be proved that for a smooth surface $S$ of degree at least $5$ in the three-dimensional projective space these two notions coincide. Also we will describe the situations in which the irrationality degree drops for surfaces that admit a dominant map to the surface $S$.