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arXiv · 1606.02232

On the $S_n$-invariant F-conjecture

Han-Bom Moon·David Swinarski
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Abstract

By using classical invariant theory, we reduce the $S_{n}$-invariant F-conjecture to a feasibility problem in polyhedral geometry. We show by computer that for $n \le 19$, every integral $S_{n}$-invariant F-nef divisor on the moduli space of genus zero stable pointed curves is semi-ample, over arbitrary characteristic. Furthermore, for $n \le 16$, we show that for every integral $S_{n}$-invariant nef (resp. ample) divisor $D$ on the moduli space, $2D$ is base-point-free (resp. very ample). As applications, we obtain the nef cone of the moduli space of stable curves without marked points, and the semi-ample cone that of the moduli space of genus 0 stable maps to Grassmannian for small numerical values.

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Han-Bom Moon, David Swinarski. 2016-06-07. On the $S_n$-invariant F-conjecture. https://arxiv.org/abs/1606.02232

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