We use a sequence of blow-ups over the projective space parametrizing plane curves of degree d to obtain some enumerative results concerning smooth plane curves of arbitrary degree. For d = 4 , this gives a first modem verification of results of H. G. Zeuthen. O. INTRODUCTION The kth 'characteristic number' of the d(dt3) -dimensional family of smooth plane curves of degree d, denoted Nd(k) in t...

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