LINEAR SYSTEMS ASSOCIATED TO UNICUSPIDAL RATIONAL PLANE CURVES

摘要

Given a unicuspidal rational curve C C P~2 with singular point P, we study the unique pencil Ac on P~2 satisfying C ∈∧c and Bs(Λc) = {P}. We show that the general member of Ac is a rational curve if and only if v-bar(C) ≥ 0, where v-bar(C) denotes the self-intersection number of C after the minimal resolution of singularities. We also show that if v(C) ≥ 0,then Ac has a dicritical of degree 1. Note that all currently known unicuspidal rational curves C ? P~2 satisfy v-bar(C) ≥ 0.