Abstract
We consider the vector bundle φ⁎TP2 where φ denotes a generically one-to-one parametrization of a rational curve D of degree dD≥2 in P2. We study a parameter aD that controls the splitting of φ⁎TP2 as a direct sum of line bundles. We find that specific properties of D, related to its singular points, characterize aD. These properties are: multiplicity, non-collinearity of triples, and construction of a curve of degree strictly smaller than dD with multiplicity bounded by the multiplicity of D at corresponding points.
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