Stability of projective varieties
-- Julius Ross, February 25, 2005

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A renewed interest in stability of projective varieties has
arisen from a conjecture relating stability to the existence of
constant scalar curvature Kahler metrics.  Starting with
various notions of stability for projective varieties I shall
state this conjecture and summarise what is known.  By analogy
with stability for sheaves, I shall describe a notion of slope
stability for varieties which is given in terms of its
subschemes and give some (un)stable examples.  I shall then
address to what extend slope stability is complete.  This is
joint work with Richard Thomas.