A Note on Rational Cuspidal curves on $\mathbb{Q}$-Homology Projective Planes

Abstract

We generalize results by Wakabayashi and Orevkov about rational cuspidal curves on the projective plane to that on $\mathbb{Q}$-homology projective planes. It turns out that the result is exactly the same as the projective plane case under suitable assumptions. We also provide examples which demonstrate sharpness of the results. The ambient surface is singular in these examples.

14 Pages. Some errors corrected. arXiv admin note: text overlap with arXiv:1512.08840

References in corpus (1)

• Classification of singular Q-homology planes. II. C^1- and C*-rulings