ramification

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Related to Ramification point: Branching point

ramification

 [ram″ĭ-fĭ-ka´shun]
1. distribution in branches.
2. a branch or set of branches.

ram·i·fi·ca·tion

(ram'i-fi-kā'shŭn),
The process of dividing into a branchlike pattern.

ram·i·fi·ca·tion

(ram'i-fi-kā'shŭn)
The process of dividing into a branchlike pattern.

ram·i·fi·ca·tion

(ram'i-fi-kā'shŭn)
Process of dividing into a branchlike pattern.
References in periodicals archive ?
In particular, none of the [[E.sub.i], [x.sub.i]]'s carries a [g.sup.1.sub.3] with triple ramification points at [x.sub.i] and at two unspecified points x, y [member of] [E.sub.i] - {[x.sub.i]}.
This implies that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has triple ramification points at distinct points [x.sub.i], x and y.
To compute F x [[bar.D].sub.2] we note that there are 80 = r(3, 3)/2 pencils L [member of] [W.sup.1.sub.3] (C) with two distinct triple ramification points. From the Hurwitz-Zeuthen formula, each such pencil has 4 more simple ramification points, thus [([[bar.D].sub.2]).sub.[psi]] = 4 x 80/(28 - 2) = 160.
Even though t [member of] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a smooth point (because there is no automorphism of X preserving all the ramification points of f), if [tau] [member of] [G.sub.6d-12] is the involution exchanging the marked points lying on [f.sub.T] (T), then [tau] x t = t.
When [gamma] [member of] {1,3}, up to isomorphism there is a unique such [f.sub.T] having 3 triple ramification points. By direct computation we have the formula:
Counting ramification points on T we quickly see that deg([f.sub.E]) = 3 and [f.sub.E] : E [right arrow] [(P.suup.1]).sub.2] is such that [f.sup.*.sub.E](0) = 3x and [f.sup.*.sub.E]([infinity]) = 3r, which gives 8 choices for [f.sub.E].
Depending on the position of the ramification points x, y [member of] X we distinguish between the following cases: