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arXiv · 1204.6156

Stratification of the moduli space of four--gonal curves

Michela Brundu·Gianni Sacchiero
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Abstract

Let $X$ be a smooth irreducible projective curve of genus $g$ and gonality 4. We show that the canonical model of $X$ is contained in a uniquely defined surface, ruled by conics, whose geometry is deeply related to that of $X$. This surface allows us to define four invariants of $X$ and hence to stratify the moduli space of four-gonal curves by means of closed irreducible subvarieties whose dimensions we compute.

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Michela Brundu, Gianni Sacchiero. 2012-10-24. Stratification of the moduli space of four--gonal curves. https://arxiv.org/abs/1204.6156

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