Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T04:48:26.586Z Has data issue: false hasContentIssue false
  • English
  • Français

A MINIMAL SET OF GENERATORS FOR THE CANONICAL IDEAL OF A NONDEGENERATE CURVE

Part of: Curves Special varieties

Published online by Cambridge University Press:  21 November 2014

WOUTER CASTRYCK  and
FILIP COOLS
WOUTER CASTRYCK
Affiliation:
Vakgroep Wiskunde, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium email [email protected]
FILIP COOLS*
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch 7701, South Africa email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give an explicit way of writing down a minimal set of generators for the canonical ideal of a nondegenerate curve, or of a more general smooth projective curve in a toric surface, in terms of its defining Laurent polynomial.

Keywords

canonical idealnondegenerate curvetoric surface

MSC classification

Primary: 14H25: Arithmetic ground fields
Secondary: 14M25: Toric varieties, Newton polyhedra
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 98 , Issue 3 , June 2015 , pp. 311 - 323
Copyright
© 2014 Australian Mathematical Publishing Association Inc. 

References

Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system. I. The user language’, J. Symbolic Comput. 24(3–4) (1997), 235–265.CrossRefGoogle Scholar
Bruns, W., Gubeladze, J. and Trung, N. V., ‘Normal polytopes, triangulations, and Koszul algebras’, J. reine angew. Math. 485 (1997), 123–160.Google Scholar
Castryck, W. and Cools, F., ‘Linear pencils encoded in the Newton polygon’, Preprint, 2014.Google Scholar
Castryck, W., Denef, J. and Vercauteren, F., ‘Computing zeta functions of nondegenerate curves’, Int. Math. Res. Pap. IMRP (2006), Art. ID 72017, 57.Google Scholar
Cox, D., Little, J. and Schenck, H., Toric Varieties, Graduate Studies in Mathematics, 124 (American Mathematical Society, Providence, RI, 2011).CrossRefGoogle Scholar
Eisenbud, D., The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry, Graduate Texts in Mathematics, 229 (Springer, New York, 2005).Google Scholar
Haase, C. and Schicho, J., ‘Lattice polygons and the number 2i + 7’, Amer. Math. Monthly 116(2) (2009), 151–165.CrossRefGoogle Scholar
Hering, M., ‘Syzygies of toric varieties’, PhD Thesis, University of Michigan, 2006.Google Scholar
Hess, F., ‘Computing Riemann–Roch spaces in algebraic function fields and related topics’, J. Symbolic Comput. 33(4) (2002), 425–445.CrossRefGoogle Scholar
Hovanskiĭ, A., ‘Newton polyhedra, and toroidal varieties’, Funkcional. Anal. i Priložen. 11(4) (1977), 56–64; 96.Google Scholar
Koelman, R. J., ‘The number of moduli of families of curves on toric surfaces’, PhD Thesis, Katholieke Universiteit Nijmegen, 1991.Google Scholar
Koelman, R. J., ‘A criterion for the ideal of a projectively embedded toric surface to be generated by quadrics’, Beiträge Algebra Geom. 34(1) (1993), 57–62.Google Scholar
Koelman, R. J., ‘Generators for the ideal of a projectively embedded toric surface’, Tohoku Math. J. (2) 45(3) (1993), 385–392.CrossRefGoogle Scholar
Saint-Donat, B., ‘On Petri’s analysis of the linear system of quadrics through a canonical curve’, Math. Ann. 206 (1973), 157–175.CrossRefGoogle Scholar
Stevens, J., ‘Rolling factors deformations and extensions of canonical curves’, Doc. Math. 6 (2001), 185–226; (electronic).CrossRefGoogle Scholar
Supplementary material: File

Castryck and Cools Supplementary Material

Supplementary Material

Download Castryck and Cools Supplementary Material(File)
File 4 KB