Counting plane curves of any genus
classification
alg-geom
math.AG
keywords
planecurvesformulagenusansweringcountingdegenerationsdegree
read the original abstract
We obtain a recursive formula answering the following question: How many irreducible, plane curves of degree d and (geometric) genus g pass through 3d-1+g general points in the plane? The formula is proved by studying suitable degenerations of plane curves.
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