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four-gonal curves

Proceedings of the Edinburgh Mathematical Society (1)

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Stratification of the Moduli Space of Four-Gonal Curves
Michela Brundu, Gianni Sacchiero
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 3 / October 2014

Published online by Cambridge University Press:

26 August 2014, pp. 631-686
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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.