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Mathematics > Algebraic Geometry

arXiv:1806.07747 (math)
[Submitted on 19 Jun 2018 (v1), last revised 21 Feb 2019 (this version, v2)]

Title:Normal projective varieties admitting polarized or int-amplified endomorphisms

Authors:Sheng Meng, De-Qi Zhang
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Abstract:Let $X$ be a normal projective variety admitting a polarized or int-amplified endomorphism $f$. We list up characteristic properties of such an endomorphism and classify such a variety from the aspects of its singularity, anti-canonical divisor and Kodaira dimension. Then we run the equivariant minimal model program with respect to not just the single $f$ but also the monoid $SEnd(X)$ of all surjective endomorphisms of $X$, up to finite-index. Several applications are given. We also give both algebraic and geometric characterizations of toric varieties via polarized endomorphisms.
Comments: Acta Mathematica Vietnamica (to appear); minor changes. arXiv admin note: text overlap with arXiv:1806.05828
Subjects: Algebraic Geometry (math.AG); Dynamical Systems (math.DS)
MSC classes: 14E30, 32H50, 08A35, 14M25
Report number: DOI: https://doi.org/10.1007/s40306-019-00333-6
Cite as: arXiv:1806.07747 [math.AG]
  (or arXiv:1806.07747v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1806.07747
Journal reference: Acta Mathematica Vietnamica, Volume 45, pages11 - 26 (2020), Special issue on: Nevanlinna theory and Complex Geometry in Honor of Le Van Thiem's Centenary

Submission history

From: Sheng Meng [view email]
[v1] Tue, 19 Jun 2018 06:37:09 UTC (14 KB)
[v2] Thu, 21 Feb 2019 15:41:14 UTC (16 KB)
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