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Two instability measures of a subspace o...

Matsushita, Jun-ichi...

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Two instability measures of a subspace of $P^{n}(K)$ under a subgroup of $\operatorname{Aut}(K)$ by Matsushita, Jun-ichi ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	08-08-2023
Summary	Let $K$ be a commutative field and let $V$ be a subspace of $P^{n}(K)$. Let $\Gamma$ be a subgroup of $\operatorname{Aut}(K)$ and let $\Gamma$ act on $P^{n}(K)$ by $\sigma((x_{i})_{0\leq i\leq n})=(\sigma(x_{i}))_{0\leq i\leq n}$ for $\sigma\in\Gamma$ and $(x_{i})_{0\leq i\leq n}\in P^{n}(K)$. In this paper, we ask `how much' unstable $V$ is under $\Gamma$ by asking how much higher or lower dimension the join and the meet of $\sigma(V)$ ($\sigma \in\Gamma$) have than $V$, and answer it in terms of the Pl\"{u}cker coordinates of $V$ and the invariant field $k$ of $\Gamma$, through presenting two `irrationality' measures of $V$ over $k$.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1603.01349

Citation

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AMA 11th EditionReferences

Matsushita, Jun-ichi. Two instability measures of a subspace of $P^{n}(K)$ under a subgroup of $\operatorname{Aut}(K)$. Australian National University. August 08, 2023. Accessed September 08, 2024. https://online.provdatabase.com/cite/12872

APA 7th EditionReferences

Matsushita, Jun-ichi. (2023). Two instability measures of a subspace of $P^{n}(K)$ under a subgroup of $\operatorname{Aut}(K)$. Australian National University. https://online.provdatabase.com/cite/12872

Chicago 17th EditionReferences

Matsushita, Jun-ichi. Two instability measures of a subspace of $P^{n}(K)$ under a subgroup of $\operatorname{Aut}(K)$. Australian National University. 2023. https://online.provdatabase.com/cite/12872

HarvardReferences

Matsushita, Jun-ichi. (2023). Two instability measures of a subspace of $P^{n}(K)$ under a subgroup of $\operatorname{Aut}(K)$. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/12872. (Accessed 08 September 2024).

Harvard AustraliaReferences

Matsushita, Jun-ichi, 2023, Two instability measures of a subspace of $P^{n}(K)$ under a subgroup of $\operatorname{Aut}(K)$, Australian National University, viewed 08 September 2024, <https://online.provdatabase.com/cite/12872>

MLA 9th EditionWorks Cited

Matsushita, Jun-ichi. Two instability measures of a subspace of $P^{n}(K)$ under a subgroup of $\operatorname{Aut}(K)$. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/12872.

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