Computational aspects of gonal maps and radical parametrization of curves

We develop in this article an algorithm that, given a projective curve C , computes a gonal map , that is, a finite morphism from C to P 1 of minimal degree. Our method is based on the computation of scrollar syzygies of canonical curves. We develop an improved version of our algorithm for curves wi...

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Bibliographic Details
Published in:Applicable algebra in engineering, communication and computing communication and computing, 2013-11, Vol.24 (5), p.313-341
Main Authors: Schicho, J., Schreyer, F.-O., Weimann, M.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Artificial Intelligence
Commutative Algebra
Computer Hardware
Computer Science
Mathematics
Original Paper
Symbolic and Algebraic Manipulation
Theory of Computation
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Summary:We develop in this article an algorithm that, given a projective curve C , computes a gonal map , that is, a finite morphism from C to P 1 of minimal degree. Our method is based on the computation of scrollar syzygies of canonical curves. We develop an improved version of our algorithm for curves with a unique gonal map and we discuss a characterization of such curves in terms of Betti numbers. Finally, we derive an efficient algorithm for radical parametrization of curves of gonality ≤ 4 .
ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-013-0205-0