

Iskovskikh Seminar
December 1, 2016 18:00, Moscow, Steklov Mathematical Institute, room 540






On the irrationality of surfaces in threedimensional projective space
(following F. Bastianelli)
K. V. Loginov^{} ^{} State University – Higher School of Economics

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Abstract:
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
threedimensional 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 $S$.

