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TOPOLOGY OF KEMPF–NESS SETS FOR ALGEBRAIC

In the theory of algebraic group actions on affine varieties, the concept of a Kempf– Ness set is used to replace the categorical quotient by the quotient with respect to a maximal compact subgroup. By making use of the recent achievements of “toric topology” we show that an appropriate notion of a Kempf–Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate subspace arrangement complements) arising in the “geometric invariant theory” approach to toric varieties. We proceed by studying the cohomology of these Kempf–Ness sets.