منابع مشابه
On Complete Arcs Arising from Plane Curves
We point out an interplay between Fq-Frobenius non-classical plane curves and complete (k, d)-arcs in P2(Fq). A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete (k, d)-arcs with parameters k = d(q − d + 2) and d = (q − 1)/(q − 1), q being a power of the characteristic. In addi...
متن کاملGroup-arcs of Prime Power Order on Cubic Curves
This article continues the characterization of elliptic curves among sets in a finite plane which are met by lines in at most three points. The case treated here is that of sets of prime-power cardinality. 1 Notation GF (q) the finite field of q elements PG(2, q) the projective plane over GF (q) PG(1)(2, q) the set of lines in PG(2, q) P(X) the point of PG(2, q) with coordinate vector X PQ the ...
متن کاملOn the Intersections of Rational Curves with Cubic Plane Curves
Let V be a generic quintic threefold in the 4-dimensional complex projective space P. A well-known conjecture of Clemens says that V has only a finite number of rational curves in each degree. Although Clemens’ conjecture is still quite open at this moment (it is known to be true for degree up to 7 by S. Katz [K]), recently physicists, based on the mirror symmetry principle, have proposed a for...
متن کاملAsymptotes, Cubic Curves, and the Projective Plane
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متن کاملEnumeration of Rational Plane Curves Tangent to a Smooth Cubic
We use twisted stable maps to compute the number of rational degree d plane curves having prescribed contacts to a smooth plane cubic.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2002
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0328