Modification

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.

See also Exceptional analytic set; Exceptional subvariety.

References

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

References

[a1]	R. Hartshorne, "Algebraic geometry" , Springer (1977) MR0463157 Zbl 0367.14001