The stability of the first Chern class under complex structural deformation
In order to prove the stability of the first Chern class's positivity(c1>0)and negativity(c1<0)under complex structural deformation other than c1=0,we considered coherent sheaf F on any connected complex space X and deduced the formula of sheaf cohomology that the stability of the first Chern class's positivity and negativity under complex structural deformation was proved.In summary,the first Chern class's c1=0,positiv-ity(c1>0)and negativity(c1<0)are all deformation stable.
deformation of complex structuresstability of deformationfirst Chern classpositivitynegativity
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