Veronese normal bundles are slope semistable, and degree-2 Veronese normal bundles split into explicit line bundles on lines and rational normal curves.
Ballico and Ellia P
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Slope semistability of Veronese normal bundles
Veronese normal bundles are slope semistable, and degree-2 Veronese normal bundles split into explicit line bundles on lines and rational normal curves.