A Kleiman criterion for GIT stack quotients
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912062255398912 |
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| author | Shoemaker, Mark |
| author_facet | Shoemaker, Mark |
| contents | Kleiman's criterion states that, for $X$ a projective scheme, a divisor $D$ is ample if and only if it pairs positively with every non-zero element of the closure of the cone of curves. In other words, the cone of ample divisors in $N^1(X)$ is the interior of the nef cone. In this paper we present an analogous statement for a variety $X$ acted on by a reductive group $G$ with a choice of $G$-linearization $L \to X$. In this new context, the ample cone of $X$ is replaced by a cell in the variation of GIT decomposition of the G-ample cone, and curves in $X$ are replaced by quasimaps to $[X/G]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_09218 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Kleiman criterion for GIT stack quotients Shoemaker, Mark Algebraic Geometry 14L24, 14N35, 14E99 Kleiman's criterion states that, for $X$ a projective scheme, a divisor $D$ is ample if and only if it pairs positively with every non-zero element of the closure of the cone of curves. In other words, the cone of ample divisors in $N^1(X)$ is the interior of the nef cone. In this paper we present an analogous statement for a variety $X$ acted on by a reductive group $G$ with a choice of $G$-linearization $L \to X$. In this new context, the ample cone of $X$ is replaced by a cell in the variation of GIT decomposition of the G-ample cone, and curves in $X$ are replaced by quasimaps to $[X/G]$. |
| title | A Kleiman criterion for GIT stack quotients |
| topic | Algebraic Geometry 14L24, 14N35, 14E99 |
| url | https://arxiv.org/abs/2211.09218 |