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arXiv · 1803.07704

On irrationality of hypersurfaces In $\mathbf{P}^{n+1}$

Ruijie Yang
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Abstract

In this note, we study various measures of irrationality for hypersurfaces in projective spaces which were recently proposed by Bastianelli, De Poi, Ein, Lazarsfeld and Ullery. In particular, we answer the question raised by Bastianelli that if $X \subset P^{n+1}$ is a very general smooth hypersurface of dimension $n$ and degree $d\geq 2n+2$, then $\text{stab.irr}(X)=\text{uni.irr}(X)=d-1$. As a corollary, we prove that $\text{irr}(X\times P^{m})=\text{irr}(X)$ for any integer $m\geq 1$.

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Ruijie Yang. 2018-03-21. On irrationality of hypersurfaces In $\mathbf{P}^{n+1}$. https://arxiv.org/abs/1803.07704

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