A generalization of Ross-Thomas' slope theory

Preprint English OPEN
Odaka, Yuji (2009)
  • Subject: 14L24, 14J17, 32Q15 | Mathematics - Algebraic Geometry | Mathematics - Differential Geometry
    arxiv: Mathematics::Differential Geometry | Mathematics::Symplectic Geometry

We give a formula of the Donaldson-Futaki invariants for certain type of semi test configurations, which essentially generalizes Ross-Thomas' slope theory. The positivity (resp. non-negativity) of those "a priori special" Donaldson-Futaki invariants implies K-stability (resp. K-semistability). We show its applicability by proving K-(semi)stability of certain polarized varieties with semi-log-canonical singularities, generalizing some results by Ross-Thomas.
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