Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Morphisms between Grassmannians

Angelo Naldi, Gianluca Occhetta

Abstract

Denote by $\mathbb G(k,n)$ the Grassmannian of linear subspaces of dimension $k$ in $\mathbb P^n$. We show that if $n>m$ then every morphism $\varphi: \mathbb G(k,n) \to \mathbb G(l,m)$ is constant.

Morphisms between Grassmannians

Abstract

Denote by the Grassmannian of linear subspaces of dimension in . We show that if then every morphism is constant.
Paper Structure (4 sections, 5 theorems, 23 equations)

This paper contains 4 sections, 5 theorems, 23 equations.

Table of Contents

  1. Introduction
  2. Divisibility
  3. Schubert calculus
  4. Proofs

Key Result

Theorem 1.1

If $n>m$ then every morphism $\varphi: \mathbb G(k,n) \to \mathbb G(l,m)$ is constant.

Theorems & Definitions (14)

  • Theorem 1.1
  • Corollary 1.2
  • Definition 2.1
  • Definition 2.2
  • Example 2.3
  • Proposition 2.4
  • proof
  • Proposition 4.1
  • proof
  • Example 4.2
  • ...and 4 more