Siu’s invariance of plurigenera: a one-tower proof

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Positivity of twisted relative pluricanonical bundles and their direct images (2014, background): “For example, if h is continuous, or more generally the multiplier ideal I(hy) = OXy on Xy with y ∈ Y0 for any integer k > 0, the invariance of plurigenera [41] and [38] verify this.”
Extension theorems, non-vanishing and the existence of good minimal models (2010, result): “The above theorem is a strong generalization of similar results available in the literature (see for example [Siu98], [Siu00], [Takayama06], [Takayama07], [HM07], [Paun07], [Claudon07], [EP07], [dFH09], [Var08], [Paun08], [Tsuji05], [HM10], [BP10]).”
A solution of an $L^{2}$ extension problem with optimal estimate and applications (2013, background): “In [51], [46] and [6], one has an L(2) extension theorem on projective families: Theorem 3.”
A solution of an L 2 extension problem with an optimal estimate and applications (2015, background): “In [51], [46] and [6], one has an L2 extension theorem on projective families:”