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Geometry of rationally connected varieties

Abstract : In this dissertation, we study several subjects on the geometry of rationally connected varieties. A complex variety is called rationally connected if for two general points, there is a rational curve passing through them. The first subject we study is the base of a Lagrangian fibration of a projective irreducible symplectic fourfold. We prove that there are at most two possibilities for the base. In the second part, we classify certain type of Fano varieties. In the end, we study the structures of singular rationally connected varieties which carry non-zero pluri-forms
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Wenhao Ou. Geometry of rationally connected varieties. Algebraic Geometry [math.AG]. Université Grenoble Alpes, 2015. English. ⟨NNT : 2015GREAM060⟩. ⟨tel-01680344v2⟩

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