Stratification of the moduli space of four--gonal curves

Michela Brundu; Gianni Sacchiero

Stratification of the moduli space of four--gonal curves

Algebraic Geometry 2012-10-25 v2

Authors: Michela Brundu , Gianni Sacchiero

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 curves moduli space canonical model ruled surface conics invariants stratification

Cite

@article{arxiv.1204.6156,
  title  = {Stratification of the moduli space of four--gonal curves},
  author = {Michela Brundu and Gianni Sacchiero},
  journal= {arXiv preprint arXiv:1204.6156},
  year   = {2012}
}

Comments

45 pages, 5 figures, submitted

Stratification of the moduli space of four--gonal curves

Abstract

Keywords

Cite

Comments

Related papers