Name
Abstract | ||
|---|---|---|
Baker's theorem is a theorem giving an upper-bound for the genus of a plane curve. It can be obtained by studying the Newton-polygon of the defining equation of the curve. In this paper we give a different proof of Baker's theorem not using Newton-polygon theory, but using elementary methods from the theory of function fields (Theorem 2.4). Also we state a generalization to several variables that can be used if a curve is defined by several bivariate polynomials that all have one variable in common (Theorem 3.3). As a side result, we obtain a partial explicit description of certain Riemann-Roch spaces, which is useful for applications in coding theory. We give several examples and compare the bound on the genus we obtain, with the bound obtained from Castelnuovo's inequality. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.ffa.2009.04.003 | Finite Fields and Their Applications |
Keywords | Field | DocType |
partial explicit description,elementary method,bivariate polynomial,newton-polygon theory,function field,certain riemann-roch space,different proof,defining equation,coding theory,plane curve,upper bound | Discrete mathematics,No-go theorem,Combinatorics,Algebra,Baker's theorem,Brouwer fixed-point theorem,Fundamental theorem,Mean value theorem,Mathematics,Compactness theorem,Danskin's theorem,Carlson's theorem | Journal |
Volume | Issue | ISSN |
15 | 5 | 1071-5797 |
Citations | PageRank | References |
1 | 0.39 | 5 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter Beelen | 1 | 116 | 15.95 |