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Algebraic geometry --- Differential geometry. Global analysis --- Noncommutative differential geometry. --- Blowing up (Algebraic geometry) --- Noncommutative differential geometry --- Alpha process (Algebraic geometry) --- Blow up (Algebraic geometry) --- Blowing up (Mathematics) --- Blowup (Algebraic geometry) --- Dilation, Monoidal --- Monoidal dilation --- Monoidal transformation --- Sigma process (Algebraic geometry) --- Transformation, Monoidal --- Singularities (Mathematics) --- Transformations (Mathematics) --- Differential geometry, Noncommutative --- Geometry, Noncommutative differential --- Non-commutative differential geometry --- Infinite-dimensional manifolds --- Operator algebras