A Hilbert-Mumford criterion for SL₂-actions

• Autorzy: Jürgen Hausen
• Języki publikacji: EN

Abstrakty

EN

Let the special linear group G : = SL₂ 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 show 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.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 97
• Numer: 2
• Strony: 151-161

Daty

wydano

2003

Twórcy

autor

Jürgen Hausen

• Mathematisches Forschungsinstitut Oberwolfach, Lorenzenhof, 77709 Oberwolfach-Walke, Germany

Identyfikatory

DOI

10.4064/cm97-2-2