A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct system of Tits buildings. We show that the Donaldson-Futaki invariant, conveniently normalized, is a continuous function on this space. We also introduce a pseudo-metric on the space of test configurations. Recall that K-stability can be enhanced by requiring that the Donaldson-Futaki invariant is positive on any admissible filtration of the co-ordinate ring. We show that admissible filtrations give rise to Cauchy sequences of test configurations with respect to the above mentioned pseudo-metric.

Codogni, G. (2019). Tits Buildings and K -Stability. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 62(3), 799-815 [10.1017/S0013091518000512].

Tits Buildings and K -Stability

Codogni G.
2019-01-01

Abstract

A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct system of Tits buildings. We show that the Donaldson-Futaki invariant, conveniently normalized, is a continuous function on this space. We also introduce a pseudo-metric on the space of test configurations. Recall that K-stability can be enhanced by requiring that the Donaldson-Futaki invariant is positive on any admissible filtration of the co-ordinate ring. We show that admissible filtrations give rise to Cauchy sequences of test configurations with respect to the above mentioned pseudo-metric.
2019
Codogni, G. (2019). Tits Buildings and K -Stability. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 62(3), 799-815 [10.1017/S0013091518000512].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/354127
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