Invariant Grassmannians and a K3 surface with an action of order 192*2
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909184406061056 |
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| author | Muller, Stevell |
| author_facet | Muller, Stevell |
| contents | Given a complex vector space $V$ of finite dimension, its Grassmannian variety parametrizes all subspaces of $V$ of a given dimension. Similarly, if a finite group $G$ acts on $V$, its invariant Grassmannian parametrizes all the $G$-invariant subspaces of $V$ of a given dimension. Based on this fact, we develop an algorithm for computing $G$-invariant projective varieties arising as an intersection of hypersurfaces of the same degree.
We apply the algorithm to find a projective model of a polarized K3 surface with a faithful action of $T_{192}\rtimes μ_2$ and some further symmetric K3 surfaces with a degree 8 polarization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_14585 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Invariant Grassmannians and a K3 surface with an action of order 192*2 Muller, Stevell Algebraic Geometry Given a complex vector space $V$ of finite dimension, its Grassmannian variety parametrizes all subspaces of $V$ of a given dimension. Similarly, if a finite group $G$ acts on $V$, its invariant Grassmannian parametrizes all the $G$-invariant subspaces of $V$ of a given dimension. Based on this fact, we develop an algorithm for computing $G$-invariant projective varieties arising as an intersection of hypersurfaces of the same degree. We apply the algorithm to find a projective model of a polarized K3 surface with a faithful action of $T_{192}\rtimes μ_2$ and some further symmetric K3 surfaces with a degree 8 polarization. |
| title | Invariant Grassmannians and a K3 surface with an action of order 192*2 |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2210.14585 |