A note on co-Higgs bundles
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 H0(TX)=H0(S2TX)=0, which implies that any co-Higgs structure of rank two is nilpotent.
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