Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668577 | Arab Journal of Mathematical Sciences | 2013 | 5 Pages |
Abstract
Let CâP2 be a smooth curve defined over a non-algebraically closed field K. We study the Lüroth semigroups of C over K, i.e. the set Lâ²(C,K) of all degrees of finite morphisms CâP1 defined over K and the set L(C,K) of all degrees >0 of some spanned line bundle on C defined over K. If K is infinite, then Lâ²(C,K) = L(C,K), but for every prime power q â  2 there is a smooth plane curve C defined over Fq with Lâ²(C,Fq)âL(C,Fq) and C(Fq)â â
. If C is a smooth plane curve, then L(C,K) determines (in several ways) if C(K)Â â Â â
.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
E. Ballico,