Sur les invariants des pinceaux de formes quintiques binaires
Meulien, Matthias
Annales de l'Institut Fourier, Tome 54 (2004), p. 21-51 / Harvested from Numdam

On décrit l’algèbre des invariants de l’action naturelle du groupe SL 2 sur les pinceaux de formes quintiques binaires.

We describe the invariant algebra of the natural action of SL 2 on pencils of binary quintic forms.

Publié le : 2004-01-01
DOI : https://doi.org/10.5802/aif.2009
Classification:  14L24,  14L30,  14H50,  13A50,  13H10,  13D40,  15A72
Mots clés: théorie géométrique des invariants, formes quintiques binaires, quintiques rationnelles gauches, séries de Poincaré, anneaux de Gorenstein
@article{AIF_2004__54_1_21_0,
     author = {Meulien, Matthias},
     title = {Sur les invariants des pinceaux de formes quintiques binaires},
     journal = {Annales de l'Institut Fourier},
     volume = {54},
     year = {2004},
     pages = {21-51},
     doi = {10.5802/aif.2009},
     mrnumber = {2069120},
     zbl = {1062.14060},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_2004__54_1_21_0}
}
Meulien, Matthias. Sur les invariants des pinceaux de formes quintiques binaires. Annales de l'Institut Fourier, Tome 54 (2004) pp. 21-51. doi : 10.5802/aif.2009. http://gdmltest.u-ga.fr/item/AIF_2004__54_1_21_0/

[And76] G. E. Andrews The theory of partitions, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, Encyclopedia of Mathematics and its Applications, Tome vol. 2 (1976) | MR 557013 | Zbl 0655.10001 | Zbl 0371.10001

[Bou87] J.-F. Boutot Singularités rationnelles et quotients par les groupes réductifs, Invent. Math, Tome 88 (1987), pp. 65-68 | MR 877006 | Zbl 0619.14029

[Bou98] N. Bourbaki Algèbre commutative, Masson (1998)

[BuE77] D. A. Buchsbaum; D. Eisenbud Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension, Amer. J. Math, Tome 99 (1977) no. 3, pp. 447-485 | MR 453723 | Zbl 0373.13006

[GrH94] P. Griffiths; J. Harris Principles of algebraic geometry, Wiley Classics Library, New York (1994) | MR 1288523 | Zbl 0836.14001

[GrY03] J. H. Grace; A. Young The algebra of invariants, Cambridge University Press (1903) | JFM 34.0114.01

[Kno89] F. Knop Der kanonische Modul eines Invariantenrings, J. Algebra, Tome 127 (1989) no. 1, pp. 40-54 | MR 1029400 | Zbl 0716.20021

[Man02] L. Manivel An extension of the Cayley-Sylvester formula (2002) (prépublication) | Zbl 1122.05095

[Meu03] M. Meulien Sur les invariants des pinceaux de quintiques binaire (2002) (thèse)

[Moo28] T. W. Moore On the invariant combinants of two binary quintics, Amer. J., Tome 50 (1928), pp. 415-430 | JFM 54.0135.01 | MR 1506678

[Mum65] D. Mumford Geometric invariant theory, Springer-Verlag, Berlin, Ergebnisse der Mathematik und ihrer Grenzgebiete, Tome vol. 34 (1965) | MR 214602 | Zbl 0147.39304

[MuU83] S. Mukai; H. Umemura Minimal rational threefolds, Algebraic geometry (Tokyo/Kyoto, 1982), Springer, Berlin (1983), pp. 490-518 | MR 726439 | Zbl 0526.14006

[New80] P. E. Newstead Invariants of binary cubics, Math. Proc. Camb. Phil. Soc, Tome 89 (1981), pp. 201-209 | MR 600237 | Zbl 0458.14006

[Pop92] V. L. Popov Groups, generators, syzygies, and orbits in invariant theory, American Mathematical Society (1992) | MR 1171012 | Zbl 0754.13005

[Sal90] G. Salmon Traité d'algèbre supérieure, Gauthier-Villars et Fils, Paris (1890) | JFM 22.0124.03

[Shi67] T. Shioda On the graded ring of invariants of binary octavics, Amer. J. Math, Tome 89 (1967), pp. 1022-1046 | MR 220738 | Zbl 0188.53304

[Spr80] T. Springer On the invariant theory of SU 2 , Indag. Math., Tome 42 (1980), pp. 339-345 | MR 587060 | Zbl 0449.22017

[Tra88] G. Trautmann Poncelet curves and associated theta characteristics, Expo. Math, Tome 6 (1988) no. 1, pp. 29-64 | MR 927588 | Zbl 0646.14025

[Ver88] J.-L. Verdier Applications harmoniques de S 2 dans S 4 . II., Harmonic mappings, twistors, and σ-models (Luminy, 1986), World Sci. Publishing, Singapore (1988), pp. 124-147 | MR 982527 | Zbl 1043.58514

[Wey93] J. Weyman Gordan ideals in the theory of binary forms, J. Algebra, Tome 161 (1993) no. 2, pp. 370-391 | MR 1247362 | Zbl 0811.13011