Birational classification of curves on rational surfaces

Alberto Calabri, Ciro Ciliberto
2010 Nagoya mathematical journal  
AbstractIn this paper we consider the birational classification of pairs (S, ℒ), withSa rational surface andℒa linear system onS. We give a classification theorem for such pairs, and we determine, for each irreducible plane curveB, itsCremona minimalmodels, that is, those plane curves which are equivalent toBvia a Cremona transformation and have minimal degree under this condition.
doi:10.1017/s0027763000022212 fatcat:oepskhgs6zclrdkr5seuhcksfm