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RESEARCH PRODUCT
Die Schmieghyperebenen an die Veronese-Mannigfaltigkeit bei Beliebiger Charakteristik
Armin Herzersubject
Section (fiber bundle)CombinatoricsAlgebraConic sectionLinear algebraPerfect fieldTangentGeometry and TopologyVariety (universal algebra)Degeneracy (mathematics)Osculating circleMathematicsdescription
By means of linear algebra a base-free definition of a Veronese variety V(n,r) is given and also an illuminating description of its osculating primes from which can be deduced in a general form and without difficulty the phenomena of degeneracy in case of small characteristics. (Instance best known: For characteristic 2 all tangents of a conic are confluent.) The last section investigates special problems for the V(1,r) in characteristic p: So the osculating primes of a V(1,p) intersect its node in a V(1,p-2). Furthermore it becomes clearer why for 2<r<¦K¦−1 no elation can fix a V(1,r) (in case of a perfect field).
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1982-12-01 | Journal of Geometry |