Abstract
A projective curve X in ℙNis said to be tangentially degenerate if a tangent line to X at a general point P meets X again at a point other than P. In this article, we prove that if X is tangentially degenerate in characteristic zero, then X is contained in a 2-plane under a certain condition on singularities of X. We also investigate a counter-example of E. Esteves and M. Homma in positive characteristic case, and present a conjecture that our investigation leads to.
Original language | English |
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Pages (from-to) | 745-752 |
Number of pages | 8 |
Journal | Bulletin of the Brazilian Mathematical Society |
Volume | 45 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2014 |
Keywords
- Gauss map
- orders
- reflexive
- tangentially degenerate
ASJC Scopus subject areas
- Mathematics(all)