A Hilbert-Mumford-Criterion for SL2-Actions
نویسنده
چکیده
Let the special linear group G := SL 2 act regularly on a Q-factorial variety X. Consider a maximal torus T ⊂ G and its normalizer N ⊂ G. We prove: If U ⊂ X is a maximal open N-invariant subset admitting a good quotient U → U/ /N with a divisorial quotient space, then the intersection W (U) of all translates g·U is open in X and admits a good quotient W (U) → W (U)/ /G with a divisorial quotient space. Conversely, we obtain that every maximal open G-invariant subset W ⊂ X admitting a good quotient W → W/ /G with a divisorial quotient space is of the form W = W (U) for some maximal open N-invariant U as above.
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