# Modification

From Encyclopedia of Mathematics

*of an analytic space*

An analytic mapping of analytic spaces such that for certain analytic sets and of smaller dimensions, the conditions

and

hold. A modification is also called a contraction of onto . 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 |

#### Comments

#### References

[a1] | R. Hartshorne, "Algebraic geometry" , Springer (1977) |

**How to Cite This Entry:**

Modification.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Modification&oldid=12008

This article was adapted from an original article by A.L. Onishchik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article