ramification

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[summation] [right arrow] C has two ramification points; these are the points where the line C hits the discriminant curve D.
11 depicts the nature of the map [pi]: W [right arrow] C in the vicinity of its ramification points. For generic line C, they are the three points where C hits the complex discriminant curve D = {[q.sup.2]/4 + [p.sup.3]/27 = 0} (see Fig.
A parameter count shows that deg([f.sub.B]) = d and p [member of] B must be a simple ramification point for [f.sub.B].
Then [n.sub.0] is the number of admissible coverings [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] R, where R is of genus 0 and X is stably equivalent to [C.sub.0] and has a 4-fold ramification point p [member of] [X.sub.reg] and triple ramification points x, y [member of] [X.sub.reg].
Then we attach a rational curve T to C at z, and we map [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] using the linear system [absolute value of [O.sub.T](2q)] in such a way that the remaining ramification point of [f.sub.T] maps to [f.sub.E](p).
[MATHEMATICAL EXPRESSION OMITTED] We can choose y,y' in such a way that they specialize to the same point [y.sub.0] [element of] [D.sub.y] [subset] Y when q specializes to a generic point of [G.sub.0]([D.sub.Y]) that is it specializes to a ramification point of [G.sup.0].
Its dimension is given by the number of the total ramification points (6 for Riemann-Hurwitz formula), minus the dimension of the group of the automorphisms of the base curve (1 because E is elliptic) and plus the dimension of the moduli space of the base curve (dim [[micro].sub.1] = 1).