Talk page
Title:
Minimal degree fibrations and the asymptotic degree of irrationality of divisors
Speaker:
Abstract:
Given a smooth, polarized, projective variety (Y,H) it is natural to ask how the degree of irrationality of hypersurfaces X in |dH| relate to the geometry of Y. For example, if X is a hypersurface in projective space of sufficiently large degree then the fibers of any map computing the degree of irrationality of X are contained in lines in projective space. In this talk I discuss joint work in preparation with Levinson and Ullery. We show that if Y is arbitrary and d is sufficiently large then any map computing the degree of irrationality of X factors through a "minimal degree fibration of Y in curves." As a consequence we can compute the asymptotic degree of irrationality of X in terms of a natural invariant of (Y,H) and we show that the degree of irrationality of general complete intersections of sufficiently unbalanced degrees 0<
Link:
Workshop: