The Castelnuovo curve is a specific type of algebraic curve that arises in algebraic geometry. More precisely, it is a smooth projective curve of genus 1, and it is defined as a complete intersection in a projective space \( \mathbb{P}^3 \). The term "Castelnuovo curve" is often associated with a general class of curves that can be embedded in projective space using certain embeddings, typically via a linear system of divisors.
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