Surjective rational maps and del Pezzo surfaces

Ilya Karzhemanov; Anna Lekontseva

Surjective rational maps and del Pezzo surfaces

Algebraic Geometry 2025-06-03 v4

Authors: Ilya Karzhemanov , Anna Lekontseva

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 $(-K_X^2) > 5$ . Some structural properties of $f$ in the case $X = \p^2$ are also established.

Keywords

del pezzo surfaces rational maps algebraic surfaces

Cite

@article{arxiv.2311.01835,
  title  = {Surjective rational maps and del Pezzo surfaces},
  author = {Ilya Karzhemanov and Anna Lekontseva},
  journal= {arXiv preprint arXiv:2311.01835},
  year   = {2025}
}

Comments

10 pages, 2 figures; v4: non-degeneracy condition added to the statement of Theorem 1.2

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