TY - JOUR
T1 - Deformation of complete intersections in the plane
AU - Shustin, Eugenii
N1 - Funding Information:
The author was partially supported by grant no. 6836-1-9 of the Israel Ministry of Science and by the Minerva Center for Geometry at Tel Aviv University.
PY - 2000/3
Y1 - 2000/3
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/0040520183
U2 - 10.1112/S002460939900658X
DO - 10.1112/S002460939900658X
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AN - SCOPUS:0040520183
SN - 0024-6093
VL - 32
SP - 177
EP - 181
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
IS - 2
ER -