Mathematics – Algebraic Geometry
Scientific paper
1995-07-07
Mathematics
Algebraic Geometry
LaTeX, 24 pages with 3 figures, author-supplied DVI file available at http://www.math.duke.edu/preprints/95-00.dvi
Scientific paper
This is an extended, renovated and updated report on a joint work which the second named author presented at the Conference on Algebraic Geometry held at Saitama University, 15-17 of March, 1995. The main result is an inequality for the numerical type of singularities of a plane curve, which involves the degree of the curve, the multiplicities and the Milnor numbers of its singular points. It is a corollary of the logarithmic Bogomolov-Miyaoka-Yau's type inequality due to Miyaoka. It was first proven by F. Sakai at 1990 and rediscovered by the authors independently in the particular case of an irreducible cuspidal curve at 1992. Our proof is based on the localization, the local Zariski--Fujita decomposition and uses a graph discriminant calculus. The key point is a local analog of the BMY-inequality for a plane curve germ. As a corollary, a boundedness criterium for a family of plane curves has been obtained. Another application of our methods is the following fact: a rigid rational cuspidal plane curve cannot have more than 9 cusps.
Orevkov S.
Zaidenberg Mikhail
No associations
LandOfFree
On the number of singular points of plane curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the number of singular points of plane curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the number of singular points of plane curves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-564967