Plane curves with ordinary multiple points and variables ordinary nodes

Abstract

Fix integers s> 0, mi > 0, 1 ≤ i ≤ s, d> 0, z ≥ 0, and s distinct points of P 2 . Let W (d; m1P1 ,...,m sPs; z) denote the set of all integral degree d plane curves with an ordinary point with multiplicity mi at each Pi and z