### Impacto

Arrondo Esteban, Enrique and Sendra, Juana and Sendra, J. Rafael
(1999)
*Genus formula for generalized offset curves.*
Journal of Pure and Applied Algebra , 136
(3).
pp. 199-209.
ISSN 0022-4049

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022404998000280

## Abstract

In this paper, we present a formula for computing the genus of irreducible generalized offset curves to projective irreducible plane curves with only affine ordinary singularities over an algebraically closed field. The formula expresses the genus of the offset by means of the degree and the genus of the original curve.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Generalized offset curves; ordinary singularities; genus; degree |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 14841 |

References: | [I] E. Arrondo, J. Sendra, J.R. Sendra, Parametric generalized offsets to hypersurfaces, J. Symbolic Comput. 23 (1997) 2677285. [2] R.T. Farouki, C.A. Neff, Analytic properties of plane offset curves, Comput. Aided Geom. Design 7 (1990) 83399. [3] R.T. Farouki, CA. Neff, Algebraic properties of plane offset curves, Comput. Aided Geom. Design 7 (1990) 100-127. [4] R. Hartshome, Algebraic Geometry, Springer, New York, 1977. [5] C. Hoffmann, Algebraic and numerical techniques for offsets and blends, in: W. Dahmen et al. (Eds.), Computation of Curves and Surfaces, Kluwer Academic Publishers, Dordrecht, 1990, pp. 4999528. [6] W. Lii, Offset-rational parametric plane curves, Comput. Aided Geom. Design 12 (1995) 601&617. [7] H. Pottman, Rational curves and surfaces with rational offsets, Comput. Aided Geom. Design 12 (1995) 175192. [S] H. Pottman, W. Lii, B. Ravani, Rational ruled surfaces and their offsets. Technical Report Nr. 23, Institut fur Geometrie, Technische Universitat Wien, 1995. [9] G. Salmon, A Treatise on the Higher Plane Curves, Chelsea, New York, 1960. [IO] E. Snapper, E. Troyer, Metric Affine Geometry, Acadamic Press, New York, 1971. [I I] R. Walker, Algebraic Curves, Princeton University Press, Princeton, NJ, 1978. |

Deposited On: | 18 Apr 2012 09:59 |

Last Modified: | 06 Feb 2014 10:10 |

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