Let S be a smooth projective rational surface and [phi] : S [right arrow] [P.sup.1] a fibration whose general fibre F is a

projective curve of genus g [greater than or equal to] 1.

Table 1 lists the results of our numerical procedure for the

projective curve corresponding to f(x, y) = 0 in Example 1.

of Notre Dame, Indiana), and Ulrich (Purdue U., Indiana) investigate the singularities of a rational

projective curve by studying a Hilbert-Burch matrix for the row vector [g1,.

a smooth and irreducible

projective curve defined over C, and let g be its genus.

(0.3) [Mathematical Expression Omitted] for M in [Mathematical Expression Omitted] for a

projective curve Y/[F.sub.q] and a smooth [Q.sub.l]-sheaf M on Y.

Let C be a smooth,

projective curve over an algebraically closed field k of genus g(C) [greater than or equal to] 2.

Coppens, The singular locus of the secant varieties of a smooth

projective curve, Arch.

The Igusa curve [X.sub.n] of level [p.sup.n] is defined to be the unique smooth

projective curve over k which contains [X.sub.n[.sup.o]] as a dense open subvariety.

Let C be a smooth

projective curve of genus g > 2 over an algebraically closed filed k.

Let k be a two dimensional local field of characteristic zero and X be a smooth

projective curve defined over k.

Let C be a smooth complex

projective curve of genus g [is greater than or equal to] 2 embedded in a projective space [P.sup.r] by a very ample line bundle N of degree d.