The singular points of a rational plane curve and its restricted tangent bundle
Let \(\phi : \mathbb{P}^1 \rightarrow \mathbb{P}^2\) be a generically one-to-one parameterization of a rational plane curve \(D \subseteq \mathbb{P}^2\) of degree \(d_D \geq 2\). Recall that \(\phi^* T_{\mathbb{P}^2}\), the pull-back to \(\mathbb{P}^1\) of the tangent bundle of \(\mathbb{P}^2\), splits as the direct sum of two line bundles. In the article under review, the author's main result shows how this splitting type depends on the minimum degree curves that are associated to \(D\). This concept of minimum degree curves, depending on the given rational parametric plane curve \(D\), is studied in some detail. A key point is that they encode invariants which relate to the singularities of \(D\). The results of the present article complement the author's earlier work [Commun. Algebra 16, No. 11, 2193--2208 (1988; Zbl 0675.14010)] as well as subsequent work of \textit{A. Gimigliano} et al. [Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 12, No. 3, 587--621 (2013; Zbl 1434.14004)].
scientific article; zbMATH DE number 7073737
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