Very ample polarized self maps extend to projective space

TL;DR

The paper proves that for a polarized self map on a projective variety, a suitable power of the map extends to an endomorphism of the ambient projective space, generalizing previous extension results.

Contribution

It establishes the existence of an extension of a polarized self map to projective space for varieties over infinite fields, broadening the scope of known extension theorems.

Findings

Existence of an integer r such that φ^r extends to P^m

Extension applies to polarized self maps with q ≥ 2

Generalizes previous extension results in algebraic geometry

Abstract

Let $X$ be a projective variety defined over an infinite field, equipped with a line bundle $L$, giving an embedding of $X$ into $\mb{P}^m$ and let $\phi: X \to X$ be a morphism such that $\phi^*L \cong L^{\otimes q}, q\geq 2$. Then there exists an integer $r>0$ extending $\phi^r$ to $\mb{P}^m$.