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It is shown that Hirzebruch’s result on the Chern classes of a complete intersection of nonsingular hypersurfaces in general position in      P N ( C ) {{\mathbf {P}}_N}({\mathbf {C}})      , is also valid for any nonsingular complete intersection. Then relations between Euler characteristic, class and Milnor number are pointed out.

On the Chern classes and the Euler characteristic for nonsingular complete intersections