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DEFORMATION OF COMPLETE INTERSECTIONS IN THE PLANE

Published online by Cambridge University Press:  01 March 2000

EUGENII SHUSTIN
EUGENII SHUSTIN
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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Abstract

We study deformations of zero-dimensional complete intersections in the plane, and prove the following results. (1) Two complex non-singular curves intersecting at r points with multiplicities d1, …, dr can be deformed into curves intersecting (at some points) with multiplicities d′1, …, d′s which are arbitrary prescribed partitions of the numbers d1, …, dr. (2) Two real curves intersecting with multiplicity at most 2 at each of their real common points can be deformed so that all real multiple intersection points split into real simple intersection points.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 2 , March 2000 , pp. 177 - 181
Copyright
© The London Mathematical Society 2000

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