# Modification

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of an analytic space

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

$$f : X \setminus S \rightarrow Y \setminus T \ \ \textrm{ is an isomorphism }$$

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.

#### References

 [1] H. Behnke, K. Stein, "Modifikation komplexer Mannigfaltigkeiten und Riemannschen Gebiete" Math. Ann. , 124 : 1 (1951) pp. 1–16