Global vector fields and their local indices on a class of fake weighted projective planes
XIN He
YAN Bingqing
Abstract：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.
Keywords：fake weighted projective planesglobal tangent vector fieldsGSV-indices
Publication Date：2024-06-15
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：7( 134-140 )