We show that there exists a unique maximal curve of genus 7 over the finite field with 49 elements, up to birational equivalence. This was the first open classification problem for maximal curves, since maximal curves over the finite fields with less than 49 elements, as well as maximal curves over the finite field with 49 elements with genus larger than 7, had been previously classified. A significant role is played by some exhaustive computer searches.
On maximal curves over finite fields of small order
GIULIETTI, Massimo;
2012
Abstract
We show that there exists a unique maximal curve of genus 7 over the finite field with 49 elements, up to birational equivalence. This was the first open classification problem for maximal curves, since maximal curves over the finite fields with less than 49 elements, as well as maximal curves over the finite field with 49 elements with genus larger than 7, had been previously classified. A significant role is played by some exhaustive computer searches.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
