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Deformation of Complete Intersections in the Plane
Author(s) -
Shustin Eugenii
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460939900658x
Subject(s) - mathematics , intersection (aeronautics) , multiplicity (mathematics) , plane curve , plane (geometry) , geometry , deformation (meteorology) , mathematical analysis , combinatorics , physics , engineering , aerospace engineering , meteorology
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 d 1 ,…, d r can be deformed into curves intersecting (at some points) with multiplicities d ′ 1 ,…, d ′ s which are arbitrary prescribed partitions of the numbers d 1 ,…, d r . (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. 1991 Mathematics Subject Classification 14M10, 14P05.