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Reference.org
Sumihiro's theorem
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<p>In <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>, Sumihiro's theorem, introduced by (Sumihiro 1974), states that a <a href="/facts/Normal_variety/TQ6cB9By">normal algebraic variety</a> with an <a href="/facts/Group_action_(mathematics)/Vh9VtUUw">action</a> of a <a href="/facts/Maximal_torus/f82Qln74">torus</a> can be <a href="/facts/Cover_(topology)/2VUdelA4">covered</a> by torus-invariant affine open subsets. </p><p>The "normality" in the hypothesis cannot be relaxed. The hypothesis that the group acting on the variety is a torus can also not be relaxed. </p>