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Abstract des Vortrages von Miguel Marco

Numerical conditions of Max Noether's theorem

Max Noether's fundamental theorem states that, in order to determine if three curves in the plane are fibers of a pencil, only local conditions need to be checked. Although those conditions rely on the structure of the local rings. In this talk we show that, in fact, only the intersection numbers of the different branches are enough to prove the result. Moreover, the statement can be generalized to other surfaces.