Geometry of the severi variety

Steven P Diaz, Joe Harris

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

This paper is concerned with the geometry of the Severi variety W parametrizing plane curves of given degree and genus, and specifically with the relations among various divisor classes on W. Two types of divisor classes on W are described: those that come from the intrinsic geometry of the curves parametrized, and those characterized by extrinsic properties such as the presence of cusps, tacnodes, hyperflexes, etc. The goal of the paper is to express the classes of the extrinsically defined divisors in terms of the intrinsic ones; this, along with other calculations such as the determination of the canonical class of W, is carried out by using various enumerative techniques. One corollary is that the variety of nodal curves of given degree and genus in the plane is affine.

Original languageEnglish (US)
Pages (from-to)1-34
Number of pages34
JournalTransactions of the American Mathematical Society
Volume309
Issue number1
DOIs
StatePublished - 1988
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Geometry of the severi variety'. Together they form a unique fingerprint.

  • Cite this