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Stratification of the Moduli Space of Four-Gonal Curves

Published online by Cambridge University Press:  26 August 2014

Michela Brundu  and
Gianni Sacchiero
Michela Brundu
Affiliation:
Dipartimento di Matematica e Geoscienze, Università di Trieste, Via Valerio 12, 34127 Trieste, Italy, (xlink:href="brundu@units.it">brundu@units.it)
Gianni Sacchiero
Affiliation:
Località S. Croce 159, 34151 Trieste, Italy, (xlink:href="naomar2009@gmail.com">naomar2009@gmail.com)
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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.

Keywords

four-gonal curvesmoduli spaceruled surfacesPrimary 14H1014N05
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 3 , October 2014 , pp. 631 - 686
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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