Uniform Trace-free Bundles of Triple Covers over Projective Planes

Studying coverings over algebraic varieties is an effective method in algebraic geometry. By combining the technique of triple cover from Miranda and Tan, we proved that if the degree of the branch divisor of a normal triple cover over ${\mathrm{\P }}^2$ is no more than $18$ and not equal to $16$, then the trace-free bundle of the triple cover is uniform. Moreover, we totally classified all these trace-free bundles.