A note on co-Higgs bundles

Published 6 Jun 2016 in math.AG | (1606.01843v1)

Abstract: We show that for any ample line bundle on a smooth complex projective variety with nonnegative Kodaira dimension, the semistability of co-Higgs bundles of implies the semistability of bundles. Then we investigate the criterion for surface $X$ to have $H^{0(T_X)=H^{0(S^2T_X)=0$,}} which implies that any co-Higgs structure of rank two is nilpotent.

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