Minimal degree fibrations in curves and the asymptotic degree of irrationality of divisors
arXiv (Cornell University)(2023)
Abstract
In this paper we study the degrees of irrationality of hypersurfaces of large degree in a complex projective variety. We show that the maps computing the degrees of irrationality of these hypersurfaces factor through rational fibrations of the ambient variety. As a consequence, we give tight bounds on the degree of irrationality of these hypersurfaces in terms of a new invariant of independent interest: the minimal fibering degree of a projective variety with respect to an effective divisor. As a corollary we show that the degree of irrationality of a complete intersection of sufficiently large and unbalanced degrees is roughly the product of the degrees. This gives a partial answer to a question of Bastianelli, De Poi, Ein, Lazarsfeld, and the third author.
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Key words
minimal degree fibrations,asymptotic degree,curves,irrationality
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