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Contraction morphism

In algebraic geometry, a contraction morphism is a surjective projective morphism f : X → Y {\displaystyle f:X\to Y} between normal projective varieties (or projective schemes) such that f ∗ O X = O Y {\displaystyle f_{*}{\mathcal {O}}_{X}={\mathcal {O}}_{Y}} or, equivalently, the geometric fibers are all connected (Zariski's connectedness theorem). It…

Birational perspective & Overview