Rational Curves on Foliated Varieties

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Foliations with positive slopes and birational stability of orbifold cotangent bundles (2015, methodology): “t C>0 such that: h0(V,kL| V ) ≤ Ckn+r,for any k≥ 0. As a consequence, the dimension of the algebraic set V is equal to n+r. Proof. The main ideas in the proof of Proposition 4.5 are the same as in [6]: for any k≥ 0, the sections of Lk on V restrict injectively to Λ, since V is its Zariski closure”
A decomposition theorem for singular spaces with trivial canonical class of dimension at most five (2016, methodology): “The geometric counterpart of Bost’s arithmetic algebraicity criterion, independently obtained by Bogomolov and McQuillan ([BM01]), and very recently extended by Campana and P˘aun ([CP15]) leads to the following algebraicity criterion.”
Higher-dimensional foliated Mori theory (2017, unknown): “2] or [BM01]”