Projections of Veronese surface and Morphisms from projective plane to Grassmannian

TL;DR

This paper describes the image of the projective plane under a morphism to a Grassmannian induced by a rank two vector bundle with specific Chern classes, contributing to algebraic geometry understanding.

Contribution

It characterizes the image of  in Gr(2, \u00C7^4) via a morphism from  associated with a rank two vector bundle with Chern classes (2,2).

Findings

Explicit description of the image of  in Gr(2, C7^4).

Analysis of the morphism induced by the vector bundle.

Insights into the geometry of the Veronese surface projection.

Abstract

In this note we describe the image of $\PP^2$ in $ Gr(2, \CC^{4})$ under a morphism given by a rank two vector bundle on $\PP^2$ with Chern classes $(2,2).$