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

A. Zinger
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Abstract

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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A. Zinger. 2002-03-06. Enumeration of Genus-Three Plane Curves with a Fixed Complex Structure. https://arxiv.org/abs/math/0203058

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