A Hilbert-Mumford criterion for SL₂-actions

@article{JürgenHausen2003,
abstract = {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.},
author = {Jürgen Hausen},
journal = {Colloquium Mathematicae},
keywords = {good quotient; algebraic group action},
language = {eng},
number = {2},
pages = {151-161},
title = {A Hilbert-Mumford criterion for SL₂-actions},
url = {http://eudml.org/doc/285131},
volume = {97},
year = {2003},
}

TY - JOUR
AU - Jürgen Hausen
TI - A Hilbert-Mumford criterion for SL₂-actions
JO - Colloquium Mathematicae
PY - 2003
VL - 97
IS - 2
SP - 151
EP - 161
AB - 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.
LA - eng
KW - good quotient; algebraic group action
UR - http://eudml.org/doc/285131
ER -