Bibliographic Details
| Title: |
Superspecial curves of genus 4 in small characteristic. |
| Authors: |
Kudo, Momonari1 m-kudo@math.kyushu-u.ac.jp, Harashita, Shushi2 harasita@ynu.ac.jp |
| Source: |
Finite Fields & Their Applications. May2017, Vol. 45, p131-169. 39p. |
| Subjects: |
Arbitrary constants, Mathematical constants, Algebra software, Macsyma (Computer software), Uniqueness (Mathematics) |
| Abstract: |
This paper contains a complete study of superspecial curves of genus 4 in characteristic p ≤ 7 . We prove that there does not exist a superspecial curve of genus 4 in characteristic 7. This is a negative answer to the genus 4 case of the problem proposed by Ekedahl [9] in 1987. This implies the non-existence of maximal curve of genus 4 over F 49 , which updates the table at manypoints.org . We give an algorithm to enumerate superspecial nonhyperelliptic curves in arbitrary p ≥ 5 , and for p ≤ 7 we execute it with our implementation on a computer algebra system Magma. Our result in p = 5 re-proves the uniqueness of maximal curves of genus 4 over F 25 , see [11] for the original theoretical proof. In Appendix, we present a general method determining Hasse–Witt matrices of curves which are complete intersections. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
