Surjective endomorphisms of projective surfaces: the existence of infinitely many dense orbits

نویسندگان

چکیده

Let $f \colon X \to X$ be a surjective endomorphism of normal projective surface. When $\operatorname{deg} f \geq 2$, applying an (iteration of) $f$-equivariant minimal model program (EMMP), we determine the geometric structure $X$. Using this, extend second author's result to singular surfaces extent that either $X$ has $f$-invariant non-constant rational function, or $f$ infinitely many Zariski-dense forward orbits; this is also extended Adelic topology (which finer than Zariski topology).

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ژورنال

عنوان ژورنال: Mathematische Zeitschrift

سال: 2023

ISSN: ['1432-1823', '0025-5874']

DOI: https://doi.org/10.1007/s00209-022-03188-0