Surjective rational maps and del Pezzo surfaces

Published 3 Nov 2023 in math.AG | (2311.01835v4)

Abstract: We study surjective (not necessarily regular) rational endomorphisms $f$ of smooth del Pezzo surfaces $X$. We prove that under certain natural non\,-\,degeneracy condition $f$ can have degree bigger than $1$ only when $(-K_X²⁾ > 5$. Some structural properties of $f$ in the case $X = \p^2$ are also established.

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