Caps on Hermitian varieties and maximal curves
نویسنده
چکیده
A lower bound for the size of a complete cap of the polar space H(n, q2) associated to the non-degenerate Hermitian variety Un is given; this turns out to be sharp for even q when n = 3. Also, a family of caps of H(n, q2) is constructed from Fq2-maximal curves. Such caps are complete for q even, but not necessarily for q odd.
منابع مشابه
One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes
We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...
متن کاملHermitian Veronesean Caps
In [4], a characterization theorem for Veronesean varieties in PG(N,K), with K a skewfield, is proved. This result extends the theorem for the finite case proved in [6]. In this paper, we prove analogous results for Hermitian varieties, extending the results obtained in the finite case in [1] in a non-trivial way.
متن کاملMAXIMAL PRYM VARIETY AND MAXIMAL MORPHISM
We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.
متن کاملSome p-ranks Related to Hermitian Varieties
We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p) and points of a nondegenerate Hermitian variety. As a corollary, we obtain new bounds for the size of caps and the existence of ovoids in finite unitary spaces. This paper is a companion to [2], in which Blokhuis and this author derive the analogous p-ranks for quadrics.
متن کاملCurves covered by the Hermitian curve
A family of maximal curves is investigated that are all quotients of the Hermitian curve. These curves provide examples of curves with the same genus, the same automorphism group and in some cases the same order sequence of the linear series associated to maximal curves, but that are not isomorphic. Dedicated with affection to Zhe-Xian Wan on the occasion of his 80-th birthday
متن کامل