Tangent bundle of $\PP^2$ and morphism from $\PP^2$ to $\text{Gr}(2, \CC^{4})$

A. El Mazouni; D. S. Nagaraj

Tangent bundle of $\PP^2$ and morphism from $\PP^2$ to $\text{Gr}(2, \CC^{4})$

Algebraic Geometry 2016-05-23 v1

Authors: A. El Mazouni , D. S. Nagaraj

Abstract

In this note we study the image of $\PP^2$ in $\text{Gr}(2, \CC^{4})$ given by tangent bundle of $\PP^2.$ We show that there is component $\mathcal{H}$ of the Hibert scheme of surfaces in $\text{Gr}(2, \CC^{4})$ with no point of it corresponds to a smooth surface.

Keywords

tangent bundle projective plane Grassmannian morphism Hilbert scheme smooth surface

Cite

@article{arxiv.1605.06234,
  title  = {Tangent bundle of $\PP^2$ and morphism from $\PP^2$ to $\text{Gr}(2, \CC^{4})$},
  author = {A. El Mazouni and D. S. Nagaraj},
  journal= {arXiv preprint arXiv:1605.06234},
  year   = {2016}
}

Comments

To appear in " proceedings of the march conference in Hyderabad. "

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