Modification

of an analytic space

An analytic mapping $f:X\to Y$ of analytic spaces such that for certain analytic sets $S\subset X$ and $T\subset Y$ of smaller dimensions, the conditions

$$f:X\setminus S\to Y\setminus T\text{ is an isomorphism }$$

and

$$f(S)=T$$

hold. A modification is also called a contraction of $S$ onto $T$. An example of a modification is a monoidal transformation.

See also Exceptional analytic set; Exceptional subvariety.

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