When does a projective curve contain a planar subcurve?

N. Chiarli, S. Greco, U. Nagel

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

If a curve contains a planar subcurve of degree r then its general hyperplane section contains a subscheme of degree r spanning a line. Here we study to which extent the converse is true. If r is small we describe counterexamples. However, we give an affirmative answer if r is large with respect to the degree of the curve. This result is achieved by studying curves which admit an irreducible two-dimensional family of r-secants. We show that such curves are forced to contain a planar subcurve of degree r unless they contain certain multiple lines. We describe the exceptional curves and give examples of them.

Original languageEnglish
Pages (from-to)345-364
Number of pages20
JournalJournal of Pure and Applied Algebra
Volume164
Issue number3
DOIs
StatePublished - Nov 8 2001

Bibliographical note

Funding Information:
During the preparation of this paper the authors were also partially supported by the University of Paderborn and the Politecnico di Torino. They thank these institutions for their hospitality.

Keywords

  • Primary 14H45
  • Secondary 14H50

ASJC Scopus subject areas

  • Algebra and Number Theory

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