仿射空间商上的环面作用

Pub Date : 2022-01-13 DOI:10.46298/epiga.2023.10073

Ana-Maria Brecan, H. Franzen

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引用次数: 0

摘要

利用线性作用的约化复代数群，研究了复向量空间中GIT商上的环面作用的不动点轨迹。我们证明，在假设$G$自由作用于稳定轨迹的情况下，不动点轨迹的分量仍然是线性子空间由Levi子群构成的GIT商。

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Torus Actions on Quotients of Affine Spaces

We study the locus of fixed points of a torus action on a GIT quotient of a complex vector space by a reductive complex algebraic group which acts linearly. We show that, under the assumption that $G$ acts freely on the stable locus, the components of the fixed point locus are again GIT quotients of linear subspaces by Levi subgroups.

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