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arXiv · 2511.18453

On Endomorphisms of Projective Algebraic Varieties

Sami al-Asaad
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Abstract

We study the algebraic dynamics of endomorphisms of projective varieties. First, we characterize their iterated images, i.e. the intersection of the images of their iterates. Next, we explore the Stein factorizations of the iterates, proving some stability phenomena they exhibit. Finally, we study endomorphisms whose iterates lie in a finite union of connected components of the endomorphism scheme, thereby completing a result of Brion.

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Sami al-Asaad. 2025-11-23. On Endomorphisms of Projective Algebraic Varieties. https://arxiv.org/abs/2511.18453

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