Geodesic
Simplest singular points of $1$-forms invariant with respect to actions of a third-order group
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2018), pp. 60-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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We classify singular points which cannot be excluded by deformations of $1$-forms invariant with respect to an action of a cyclic group of order $3$. It is proved that for $\mathbb{Z}_3$-invariant $1$-forms the equivariant index of a singular point as an element of the representation ring of the group coincides with the class of the representation on the space of germs of the highest order forms factorized by the subspace of forms divisible by the given $1$-form. 
@article{VMUMM_2018_5_a7,
     author = {F. I. Mamedova},
     title = {Simplest singular points of $1$-forms invariant with respect to actions of a third-order group},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {60--63},
     year = {2018},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_5_a7/}
}
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F. I. Mamedova. Simplest singular points of $1$-forms invariant with respect to actions of a third-order group. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2018), pp. 60-63. http://geodesic.mathdoc.fr/item/VMUMM_2018_5_a7/

[1] Ebeling W., Gusein-Zade S.M., Seade J., “Homological index for 1-forms and a Milnor number for isolated singularities”, Int. J. Math., 15:9 (2004), 895–905 | DOI | MR | Zbl

[2] Gómez-Mont X., “An algebraic formula for the index of a vector field on a hypersurface with an isolated singularity”, J. Algebraic Geom., 7:4 (1998), 731–752 | MR | Zbl

[3] Ebeling W., Gusein-Zade S.M., “Equivariant indices of vector fields and 1-forms”, Eur. J. Math., 1:2 (2015), 286–301 | DOI | MR | Zbl

[4] Gusein-Zade S.M., Mamedova F.I., “Ob ekvivariantnykh indeksakh 1-form na mnogoobraziyakh”, Funkts. anal. i pril., 51:3 (2017), 22–32 | DOI | MR | Zbl