Sur les invariants des pinceaux de formes quintiques binaires
Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 21-51.

On décrit l’algèbre des invariants de l’action naturelle du groupe SL2 sur les pinceaux de formes quintiques binaires.

We describe the invariant algebra of the natural action of SL2 on pencils of binary quintic forms.

DOI : 10.5802/aif.2009
Classification : 14L24, 14L30, 14H50, 13A50, 13H10, 13D40, 15A72
Mot clés : théorie géométrique des invariants, formes quintiques binaires, quintiques rationnelles gauches, séries de Poincaré, anneaux de Gorenstein
Keywords: geometric invariant theory, binary quintic forms, rational quintic, space curves, Poincaré series, Gorenstein rings
Meulien, Matthias 1

1 Chennai Mathematical Institute, 92 G. N. Chetty Road, Chennai 600 017 (Inde)
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Meulien, Matthias. Sur les invariants des pinceaux de formes quintiques binaires. Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 21-51. doi : 10.5802/aif.2009. https://www.numdam.org/articles/10.5802/aif.2009/

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

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

[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, Volume 99 (1977) no. 3, pp. 447-485 | MR | Zbl

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

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

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

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

[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., Volume 50 (1928), pp. 415-430 | JFM | MR

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

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

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

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

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

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

[Spr80] T. Springer On the invariant theory of SU2, Indag. Math., Volume 42 (1980), pp. 339-345 | MR | Zbl

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

[Ver88] J.-L. Verdier Applications harmoniques de S2 dans S4. II., Harmonic mappings, twistors, and σ-models (Luminy, 1986) (1988), pp. 124-147 | MR | Zbl

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

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