Geodesic
GSV-indices as residues
Journal of Singularities, Tome 9 (2014), pp. 206-218

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We introduce a local invariant for a vector field v on a complete intersection V with an isolated singularity as the residue of the relevant Chern class of the ambient tangent bundle by a frame consisting of v and some natural meromorphic vector fields associated with defining functions of V. We then show that the residue coincides with the GSV-index as well as the virtual index of v so that it provides another interpretation of these indices. As an application, we give an algebraic formula for the GSV-indices of holomorphic vector fields on singular curves. 
@article{10_5427_jsing_2014_9p,
     author = {Tatsuo Suwa},
     title = {GSV-indices as residues},
     journal = {Journal of Singularities},
     pages = {206--218},
     publisher = {mathdoc},
     volume = {9},
     year = {2014},
     doi = {10.5427/jsing.2014.9p},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.9p/}
}
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Tatsuo Suwa. GSV-indices as residues. Journal of Singularities, Tome 9 (2014), pp. 206-218. doi: 10.5427/jsing.2014.9p

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