Global vector fields and their local indices on a class of fake weighted projective planes
We give all the global tangent vector fields on four Gorenstein fake weighted projective planes with singularities,and by making use of the generalized Poincaré-Hopf theorem we prove the GSV-indices for some characteristic global vector fields at each of the singularities on these surfaces are equal to 1+μ,where μ is the Milnor number of the singularity.Unlike the smooth manifolds case,the computation of local indices for vector fields with isolated zeros on singular analytic varieties is difficult in general.Our work provides a concrete example with respect to this issue.
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