PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle
Algebraic Geometry
2014-05-13 v1
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.
Keywords
Cite
@article{arxiv.1405.2753,
title = {PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle},
author = {Alberto Alzati and Riccardo Re},
journal= {arXiv preprint arXiv:1405.2753},
year = {2014}
}