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Showing papers by "J. W. P. Hirschfeld published in 2010"

Journal Article•DOI•
Configurations of points and lines(Graduate Studies in Mathematics 103)ByBranko Grünbaum: 399 pp., US$75.00, 978-0-8218-4308-6 (American Mathematical Society, Providence, RI, 2009)

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J. W. P. Hirschfeld1•
University of Sussex1
01 Dec 2010-Bulletin of The London Mathematical Society

18 citations

Curves of genus 3

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J. W. P. Hirschfeld
01 Jan 2010
TL;DR: In this paper, the maximum number of points on a plane quartic curve over a finite field is discussed, and the question of how to find the maximum points on such a curve over finite fields is discussed.
Abstract: Any curve of genus 3 can be represented as a plane quartic curve. The question of the maximum number of points on such a curve over a finite field is discussed.

5 citations

Families of curves covered by the Hermitian curve

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Massimo Giulietti, J. W. P. Hirschfeld, Gábor Korchmáros, Fernando Torres
01 Mar 2010
TL;DR: For the case m = 2, the Hermitian curve was shown to be K-maximal in this paper, and the non-singular K-models of these curves were shown to have the same genus and the same automorphism group.
Abstract: Let K be the finite field of order $q^2$. For every positive divisor m of q+1 for which d =(q+1)/m is prime, the plane curves C with the given affine equation are covered by the Hermitian curve. The non-singular K-models of these curves are K-maximal and provide examples of non-isomorphic curves with the same genus and the same automorphism group. The case m=2 was previously investigated by the authors.

4 citations