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Finiteness of null subvarieties and optimal destabilizers for the J-equation
Let $X$ be a compact Kähler manifold and $(α,β)$ be a pair of Kähler classes. We show that when $(α,β)$ is $J$-semistable, the collection of positive-dimensional irreducible $J$-null subvarieties is finite. We also obtain a uniform positive lower bound for the normalized $J$-slope of every irreducib
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