TY - JOUR
T1 - On the tangentially degenerate curves, II
AU - Kaji, Hajime
N1 - Publisher Copyright:
© 2014, Sociedade Brasileira de Matemática.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2014/12
Y1 - 2014/12
N2 - 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.
AB - 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.
KW - Gauss map
KW - orders
KW - reflexive
KW - tangentially degenerate
UR - http://www.scopus.com/inward/record.url?scp=84920200627&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84920200627&partnerID=8YFLogxK
U2 - 10.1007/s00574-014-0072-8
DO - 10.1007/s00574-014-0072-8
M3 - Article
AN - SCOPUS:84920200627
VL - 45
SP - 745
EP - 752
JO - Bulletin of the Brazilian Mathematical Society
JF - Bulletin of the Brazilian Mathematical Society
SN - 1678-7544
IS - 4
ER -