Morphisms from P2 to Gr(2,C4)

TL;DR

This paper investigates morphisms from the projective plane to the Grassmannian of 2-planes in 4-dimensional complex space, analyzing their cohomology classes and implications for embeddings into projective space.

Contribution

It provides new insights into the cohomology classes of such morphisms and their relation to projections of d-uple embeddings of P2 into P5.

Findings

Characterization of morphisms via cohomology classes

Results on projections of d-uple embeddings of P2

Connections between morphisms and Grassmannian geometry

Abstract

In this note we study morphisms from P2 to Gr(2,C4) from the point of view of the cohomology class they represent in the Grassmannian. This leads to some new result about projection of d-uple imbedding of P2 to P5.