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arXiv · 2304.09963

Minimal degree fibrations in curves and the asymptotic degree of irrationality of divisors

Jake Levinson·David Stapleton·Brooke Ullery
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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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Jake Levinson, David Stapleton, Brooke Ullery. 2023-04-19. Minimal degree fibrations in curves and the asymptotic degree of irrationality of divisors. https://arxiv.org/abs/2304.09963

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