Instability of polarised algebraic varieties

Julius Ross
By analogy with the definition for sheaves, we define the slope of a polarised algebraic variety and of each of its subschemes. This gives a notion of slope stability, which we show is a necessary condition for K-stability. We also give the modifications needed to get a necessary condition for asymptotic Chow stability. We then give various calculations of slope and concrete examples. These examples have been chosen to be of interest to the conjectured...
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