Tangent bundle of \PP² and morphism from \PP² to Gr(2, \CC⁴)

2016/05/20 by Mazouni, A. El, Nagaraj, D. S.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.06234

Abstract

In this note we study the image of \PP² in Gr(2, \CC⁴) given by tangent bundle of \PP². We show that there is component H of the Hibert scheme of surfaces in Gr(2, \CC⁴) with no point of it corresponds to a smooth surface.

Related

• Projections of Veronese surface and Morphisms from projective plane to Grassmannian
• Geometry of ℙ² blown up at seven points
• Hyperplane sections of projective bundle associated to the tangent bundle of ℙ².
• About the stability of the tangent bundle of Pⁿ restricted to a surface
• A connected component of the moduli space of surfaces of general type with p_g=0