On décrit l’algèbre des invariants de l’action naturelle du groupe sur les pinceaux de formes quintiques binaires.
We describe the invariant algebra of the natural action of on pencils of binary quintic forms.
@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] 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] Singularités rationnelles et quotients par les groupes réductifs, Invent. Math, Tome 88 (1987), pp. 65-68 | MR 877006 | Zbl 0619.14029
[Bou98] Algèbre commutative, Masson (1998)
[BuE77] 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] Principles of algebraic geometry, Wiley Classics Library, New York (1994) | MR 1288523 | Zbl 0836.14001
[GrY03] The algebra of invariants, Cambridge University Press (1903) | JFM 34.0114.01
[Kno89] Der kanonische Modul eines Invariantenrings, J. Algebra, Tome 127 (1989) no. 1, pp. 40-54 | MR 1029400 | Zbl 0716.20021
[Man02] An extension of the Cayley-Sylvester formula (2002) (prépublication) | Zbl 1122.05095
[Meu03] Sur les invariants des pinceaux de quintiques binaire (2002) (thèse)
[Moo28] On the invariant combinants of two binary quintics, Amer. J., Tome 50 (1928), pp. 415-430 | JFM 54.0135.01 | MR 1506678
[Mum65] Geometric invariant theory, Springer-Verlag, Berlin, Ergebnisse der Mathematik und ihrer Grenzgebiete, Tome vol. 34 (1965) | MR 214602 | Zbl 0147.39304
[MuU83] Minimal rational threefolds, Algebraic geometry (Tokyo/Kyoto, 1982), Springer, Berlin (1983), pp. 490-518 | MR 726439 | Zbl 0526.14006
[New80] Invariants of binary cubics, Math. Proc. Camb. Phil. Soc, Tome 89 (1981), pp. 201-209 | MR 600237 | Zbl 0458.14006
[Pop92] Groups, generators, syzygies, and orbits in invariant theory, American Mathematical Society (1992) | MR 1171012 | Zbl 0754.13005
[Sal90] Traité d'algèbre supérieure, Gauthier-Villars et Fils, Paris (1890) | JFM 22.0124.03
[Shi67] On the graded ring of invariants of binary octavics, Amer. J. Math, Tome 89 (1967), pp. 1022-1046 | MR 220738 | Zbl 0188.53304
[Spr80] On the invariant theory of , Indag. Math., Tome 42 (1980), pp. 339-345 | MR 587060 | Zbl 0449.22017
[Tra88] Poncelet curves and associated theta characteristics, Expo. Math, Tome 6 (1988) no. 1, pp. 29-64 | MR 927588 | Zbl 0646.14025
[Ver88] Applications harmoniques de dans . II., Harmonic mappings, twistors, and -models (Luminy, 1986), World Sci. Publishing, Singapore (1988), pp. 124-147 | MR 982527 | Zbl 1043.58514
[Wey93] Gordan ideals in the theory of binary forms, J. Algebra, Tome 161 (1993) no. 2, pp. 370-391 | MR 1247362 | Zbl 0811.13011