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arXiv · 1907.13084

Tilt stability and the degree of irrationality of surfaces on threefolds

Geoffrey Smith
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Abstract

Let $S$ be a smooth projective surface on a smooth threefold $X$ such that $X$ has Picard rank 1 and NS$(S)$ is generated by the restriction of divisors from X. We show that if $X$ satisfies the Bogomolov-Gieseker type inequality for tilt semistable objects conjectured by Bayer-Macr\`i-Stellari, then the minimum degree of a dominant rational map $S\dashrightarrow\mathbb{P}^2$ is either relatively large or determined by a net of curves of low degree on $S$. As one application, we prove that the complete intersection of three very general quadrics in $\mathbb{P}^5$ has degree of irrationality 4.

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Geoffrey Smith. 2019-07-30. Tilt stability and the degree of irrationality of surfaces on threefolds. https://arxiv.org/abs/1907.13084

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