Let be the points in with coordinates
respectively. We prove that, for any genus , a plane curve of degree having a -tuple point at , and a -tuple point at , and no other singularities, exists and that the general plane curve of that degree and with those singularities is a Brill–Noether–Petri general curve of genus .
Cite this article
Enrico Arbarello, Andrea Bruno, Gavril Farkas, Giulia Saccà, Explicit Brill–Noether–Petri general curves. Comment. Math. Helv. 91 (2016), no. 3, pp. 477–491DOI 10.4171/CMH/392