紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2014, 51(2), p. 481-511

LINEAR SYSTEMS ASSOCIATED TO UNICUSPIDAL RATIONAL PLANE CURVES

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2014-04

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

10.18910/29206

29206

LINEAR SYSTEMS ASSOCIATED TO UNICUSPIDAL RATIONAL PLANE CURVES

Osaka University and Osaka City University, Departments of Mathematics

英語

2014-04

Osaka Journal of Mathematics

51

2

481

511

https://hdl.handle.net/11094/29206

10.18910/29206

https://doi.org/10.18910/29206