Let p1;⋯; pg be the points in A2.(ℚ ⊂ ℙ2.(ℚ) with coordinates (equation Presented) respectively. We prove that, for any genus g, a plane curve of degree 3g having a g-tuple point at p1;⋯; p8, and a (g - 1)-tuple point at pg, 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 g.
Arbarello, E., Bruno, A., Farkas, G.M., Saccà, G. (2016). Explicit brill-noether-petri general curves. COMMENTARII MATHEMATICI HELVETICI, 91(3), 477-491 [10.4171/CMH/392].
Explicit brill-noether-petri general curves
BRUNO, Andrea;FARKAS, GAVRIL MARIUS;
2016-01-01
Abstract
Let p1;⋯; pg be the points in A2.(ℚ ⊂ ℙ2.(ℚ) with coordinates (equation Presented) respectively. We prove that, for any genus g, a plane curve of degree 3g having a g-tuple point at p1;⋯; p8, and a (g - 1)-tuple point at pg, 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 g.File in questo prodotto:
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