Stratification of the Moduli Space of Four-Gonal Curves. Issue 3 (30th June 2014)

• Record Type: Journal Article
• Authors: Brundu, Michela; Sacchiero, Gianni
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 57:Issue 3(2014)
• Page Start: 1
• Page End: 56
• Publication Date: 2014-06-30
• Subjects: four-gonal curves, -- moduli space, -- ruled surfaces; Primary 14H10, -- 14N05; Mathematics -- Periodicals; 510
• DOI: 10.1017/S001309151300062X
• Languages: English
• ISSNs: 0013-0915

Abstract

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.