A Theory of Duality for Algebraic Curves

Details A Theory of Duality for Algebraic Curves A Theory of Duality for Algebraic Curves

2010-03-30

arxiv.org/abs/1003.5837v1

Mathematics

Algebraic Geometry

Scientific paper

We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of duality, we prove generalisations of Plucker's formulae for algebraic curves. The results hold for arbitrary characteristic of the base field L, with some occasional exceptions when characteristic(L)=2, which we observe in the course of the paper.

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