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Exposé II A: On general hyperplane sections of very strange projective curves and the uniform position property. (English) Zbl 0869.14012

Geramita, Anthony V. (ed.), The curves seminar at Queen’s. Vol. X. Lectures held in Genova, Italy, Spring 1995 and Kingston, Ontario, Canada, Fall 1995. Kingston: Queen’s University. Queen’s Pap. Pure Appl. Math. 102, 131-135 (1996).
Let \(C\) be a projective curve and let \(H\) be a general hyperplane section of \(C\). In characteristic 0, it is well known that all the subsets of \(C\), with fixed degree, are equivalent from a geometric point of view: This is the so called “uniform position principle”. The principle fails in general, in positive characteristic, for “very strange” curves, i.e. curves whose tangent lines meet in a point. The authors outline here an axiomatic study of the uniform position properties for very strange curves and their general linear projections.
For the entire collection see [Zbl 0844.00015].

MSC:

14H45 Special algebraic curves and curves of low genus
14G15 Finite ground fields in algebraic geometry
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14F45 Topological properties in algebraic geometry
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