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GIT-equivalence and diagonal actions. (English. Russian original) Zbl 1244.14034

Math. Notes 90, No. 2, 250-259 (2011); translation from Mat. Zametki 90, No. 2, 269-279 (2011).
Let \(V\) be a finite dimensional vector space over the field of complex numbers. The author constructs the GIT-fans for the diagonal actions of \({\mathrm {SL}}(V)\) on \({\mathbb P}(V)^{m_1}\times {\mathbb P}(V^*)^{m_2}\) and, for \(\dim V\geqslant 3\), of \({\mathrm {SO}}(V)\) on \({\mathbb P}(V)^m\).

MSC:

14L30 Group actions on varieties or schemes (quotients)
14L24 Geometric invariant theory
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References:

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