On Affine Surface That can be Completed by A Smooth Curve

被引：0
作者：
Lesfari A. [1 ]
机构：
[1] Département de Mathématiques, Université Chouaïb Doukkali Faculté des Sciences, B.P. 20, El Jadida
来源：
Results in Mathematics | 1999年 / 35卷 / 1-2期
关键词：
14C17; 14E15; 14H40; 58F07; Abelian variety; compactification; intersection;
D O I：
10.1007/BF03322026
中图分类号：
学科分类号：
摘要：
In C6, we consider a non linear system of differential equations with four invariants: two quadrics, a cubic and a quartic. Using Enriques-Kodaira classification of algebraic surfaces, we show that the affine surface obtained by setting these invariants equal to constants is the affine part of an abelian surface. This affine surface is completed by gluing to it a one genus 9 curve consisting of two isomorphic genus 3 curves intersecting transversely in 4 points. © 1999, Birkhäuser Verlag, Basel.
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页码：107 / 118
页数：11
相关论文
共 22 条
[1]  
M A., van P M., The algebraic integrability of geodesic flow on SO(4), Invent. Math., 67, pp. 297-331, (1982)
[2]  
Arbarello E., Cornalba M., Griffiths P., Harris J., Geometry of algebraic curves, vol, I, Springer-Verlag, Grundbehren der mathematischen Wissenschaften, 267, (1985)
[3]  
Barth W., Abelian surfaces with (1,2)-polarization. Conf. on alg. Geom. Sendai (1985), Adv. Studies in Pure Math., 10, pp. 41-84, (1987)
[4]  
Griffiths P., Harris J., Principles of algebraic geometry, (1978)
[5]  
Haine L., Geodesic flow on SO(4) and abelian surfaces, Math. Ann., 263, pp. 435-472, (1983)
[6]  
Hille E., Ordinary differential equations in the complex domain, (1976)
[7]  
Hironaka H., Resolution of singularities of an algebraic variety over a field of characteristic zero, Annals of Math., 79, I, pp. 109-203, (1964)
[8]  
Iitaka S., Algebraic geometry, An introduction to birational geometry of algebraic varieties, (1981)
[9]  
Kowalewski S., Sur le problème de la rotation d’un corps solide autour d’un point fixe, Acta Math., 12, pp. 177-232, (1889)
[10]  
Lesfari A., Une approche systématique à la résolution du corps solide de Kowalewski, C.R. Acad. Sc. Paris, t., 302, pp. 347-350, (1986)
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