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On the Diameter of Plane Curves

Published online by Cambridge University Press:  04 December 2007

SHIH-TSAI FENG  and
GEORG SCHUMACHER
SHIH-TSAI FENG
Affiliation:
Max-Planck-Institute for Mathematics in the Sciences (MIS), Inselstr. 22-26, D-04103 Leipzig, Germany;
GEORG SCHUMACHER
Affiliation:
Fachbereich Mathematik Und Informatik, Philipps-Universität, D-35032 Marburg, Germany; e-mail: schumac@mathematik.uni-marburg.de
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Abstract

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Recently, differential geometric properties of embedded projective varieties have gained increasing interest. In this note, we consider plane algebraic curves equipped with the Fubini–Study metric from${\mirrored P}$$_2$(${\mirrored C}$) and give an estimate for the diameter in terms of the degree, initiated in a paper by F. A. Bogomolov.

Keywords

diameterplane curveFubini–Study metric.
Type
Research Article
Information
Compositio Mathematica , Volume 119 , Issue 3 , December 1999 , pp. 331 - 334
Copyright
© 1999 Kluwer Academic Publishers