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Topology of Kempf-Ness sets for algebraic torus actions

Taras Panov
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Abstract

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 Batyrev-Cox "geometric invariant theory" approach to toric varieties. We proceed by studying the cohomology of these "toric" Kempf-Ness sets. In the case of projective non-singular toric varieties the Kempf-Ness sets can be described as complete intersections of real quadrics in a complex space.

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Taras Panov. 2008-10-08. Topology of Kempf-Ness sets for algebraic torus actions. https://arxiv.org/abs/math/0603556

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