Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T18:07:38.487Z Has data issue: false hasContentIssue false
  • English
  • Français

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="[email protected]">[email protected])
Gianni Sacchiero
Affiliation:
Località S. Croce 159, 34151 Trieste, Italy, (xlink:href="[email protected]">[email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

1.Arbarello, E. and Cornalba, M., Footnotes to a paper of Beniamino Segre, Math. Ann. 256 (1981), 341–362.CrossRefGoogle Scholar
2.Arbarello, E., Cornalba, M., Griffiths, P. A. and Harris, J., Geometry of algebraic curves Volume I (Springer, 1985).Google Scholar
3.Badescu, L., Algebraic surfaces, Universitext (Springer, 2001).CrossRefGoogle Scholar
4.Brundu, M. and Sacchiero, G., On the varieties parametrizing trigonal curves with assigned Weierstrass points, Commun. Alg. 26(10) (1998), 3291–3312.Google Scholar
5.Brundu, M. and Sacchiero, G., On rational surfaces ruled by conics, Commun. Alg. 31(8) (2003), 3631–3652.CrossRefGoogle Scholar
6.Brundu, M. and Sacchiero, G., On the singularities of surfaces ruled by conics, Commun. Alg. 42(5) (2014), 1857–1879.Google Scholar
7.Friedman, R., Algebraic surfaces and holomorphic vector bundles, Universitext (Springer, 1998).Google Scholar
8.Fulton, W., Intersection theory (Springer, 1998).CrossRefGoogle Scholar
9.Harris, J., The genus of space curves, Math. Ann. 249 (1980), 191–204.CrossRefGoogle Scholar
10.Harris, J., Algebraic geometry, Graduate Texts in Mathematics, Volume 133 (Springer, 1992).CrossRefGoogle Scholar
11.Hartshorne, R., Algebraic geometry, Graduate Texts in Mathematics, Volume 52 (Springer, 1977).Google Scholar
12.Schreyer, F. O., Syzygies of canonical curves and special linear series, Math. Ann. 275 (1986), 105–137.Google Scholar
13.Segre, B., Sui moduli delle curve poligonali e sopra un complemento al teorema di esistenza di Riemann, Math. Ann. 100 (1928), 537–551.Google Scholar
14.Storh, K. O. and Viana, P., Weierstrass gap sequences and moduli varieties of trigonal curves, J. Pure Appl. Alg. 81 (1992), 63–82.Google Scholar