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- Title
THE LOCUS OF SMOOTH PLANE CURVES WITH A SEXTACTIC POINT.
- Authors
FARAHAT, M. A.
- Abstract
Let Mg be the moduli space of isomorphism classes of genus g smooth curves over ℂ. We show that the locus S2d-r ⊂ Mg whose general points represent smooth plane curves of degree d ≥ 4 with a sextactic point of sextactic order 2d - r, where r ∈ {0, 1, 2}, is an irreducible and rational subvariety of codimension d(d - 4) + 2 - r of Mg. These results generalize those results introduced by the author in case of quartic curves (see K. Alwaleed and M. Farahat, The locus of smooth quartic curves with a sextactic point, Appl. Math. Inf. Sci. 7(2) (2013) 509-513).
- Subjects
LOCUS (Mathematics); PLANE curves; MODULI theory; ISOMORPHISM (Mathematics); IRREDUCIBLE polynomials; QUARTIC curves; MATHEMATICAL analysis
- Publication
Journal of Algebra & Its Applications, 2014, Vol 13, Issue 1, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498813500795