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EXTENSION THEOREMS, NONVANISHING AND THE EXISTENCE OF GOOD MINIMAL MODELS
"... Abstract. We prove an extension theorem for effective plt pairs (X,S +B) of nonnegative Kodaira dimension κ(KX + S + B) ≥ 0. The main new ingredient is a refinement of the OhsawaTakegoshi L 2 extension theorem involving singular hermitian metrics. 1. ..."
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Abstract. We prove an extension theorem for effective plt pairs (X,S +B) of nonnegative Kodaira dimension κ(KX + S + B) ≥ 0. The main new ingredient is a refinement of the OhsawaTakegoshi L 2 extension theorem involving singular hermitian metrics. 1.
A UNIVERSAL METRIC FOR THE CANONICAL BUNDLE OF A HOLOMORPHIC FAMILY OF PROJECTIVE ALGEBRAIC MANIFOLDS
"... In his celebrated work [S98, S02], Siu proved that the plurigenera of any algebraic manifold are invariant in families. More precisely, let π: X → D be a holomorphic submersion (i.e., dπ is nowhere zero) from a complex manifold X to the unit disk D, and assume that every fiber Xt: = π−1 (t) is a c ..."
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In his celebrated work [S98, S02], Siu proved that the plurigenera of any algebraic manifold are invariant in families. More precisely, let π: X → D be a holomorphic submersion (i.e., dπ is nowhere zero) from a complex manifold X to the unit disk D, and assume that every fiber Xt: = π−1 (t) is a compact projective manifold. Then for every m ∈ N, the function Pm: D → N