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arxiv: math/0203058 · v1 · submitted 2002-03-06 · 🧮 math.SG · math.AG

Enumeration of Genus-Three Plane Curves with a Fixed Complex Structure

classification 🧮 math.SG math.AG
keywords curvesplanecomplexfixedgenus-threestructurecountingcusp
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We give a practical formula for counting irreducible nodal genus-three plane curves that a fixed generic complex structure on the normalization. As an intermediate step, we enumerate rational plane curves that have a $(3,4)$-cusp.

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