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INTRODUCTION In this paper we investigate to which extent the theory of Severi on nodal plane curves of a given degree d extends to a linear system on a complex projective nonsingular algebraic surface. As well known, in [S], Anhang F Severi proved that for every d ≥ 3 and 0 ≤ δ ≤ d−1
The geometry of a desingularization Y m of an arbitrary subvariety of a generic hypersurface X n in an ambient variety W (e.g. W = P n+1) has received much attention over the past decade or so. Clemens [CKM] has proved that for m = 1, n = 2, W = P 3 and X of degree d, Y has genus g ≥ 1 + d(d − 5)/2 and Xu [X] improved this to g ≥ d(d − 3)/2 − 2 for d ≥ 5(More)