PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle

Alberto Alzati; Riccardo Re

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arXiv · 1405.2753

PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle

Alberto Alzati·Riccardo Re

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Abstract

We give an explicit parametrization of the Hilbert schemes of rational curves C in P^n having a given splitting type of the restricted tangent bundle from P^n to C. The adopted technique uses the description of such curves as projections of a rational normal curve from a suitable linear vertex and a classification of those vertices that correspond to the required splitting type of the restricted tangent bundle. This classification involves the study of a suitable PGL(2) action on the relevant Grassmannian variety.

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BibTeX RIS

Alberto Alzati, Riccardo Re. 2014-05-12. PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle. https://arxiv.org/abs/1405.2753

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