A Hilbert-Mumford-Criterion for SL2-Actions

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HAUSEN, Jürgen, 2002. A Hilbert-Mumford-Criterion for SL2-Actions

@unpublished{Hausen2002Hilbe-6431, title={A Hilbert-Mumford-Criterion for SL2-Actions}, year={2002}, author={Hausen, Jürgen} }

A Hilbert-Mumford-Criterion for SL2-Actions Let the special linear group G := SL2 act regularly on a Q-factorial variety X. Consider a maximal torus T subset G and its normalizer N subset G. We prove: If U subset 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 subset 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. Attribution-NonCommercial-NoDerivs 2.0 Generic Hausen, Jürgen 2011-03-24T16:12:41Z application/pdf Hausen, Jürgen 2002 2011-03-24T16:12:41Z eng

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