Local Parameter - Definition

Definition

Let C be an algebraic curve defined over an algebraically closed field K, and let K(C) be the field of rational functions of C. The valuation on K(C) corresponding to a smooth point is defined as, where is the usual valuation on the local ring (, ). A local parameter for C at P is a function such that .

Read more about this topic:  Local Parameter

Famous quotes containing the word definition:

    The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.
    Jean Baudrillard (b. 1929)

    The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.
    Samuel Taylor Coleridge (1772–1834)

    Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.
    Nadine Gordimer (b. 1923)