Polarized endomorphisms of complex normal varieties
Noboru Nakayama, De-Qi Zhang
TL;DR
This paper investigates complex normal projective varieties with non-isomorphic quasi-polarized endomorphisms, revealing their geometric structure and showing such varieties have non-positive Kodaira dimension.
Contribution
It provides a detailed analysis of the structure of varieties admitting these endomorphisms, extending understanding of their geometric properties and Kodaira dimension constraints.
Findings
Varieties with such endomorphisms have non-positive Kodaira dimension
The geometric structure is characterized via equivariant lifting and fibrations
Specific results for endomorphisms of projective spaces are included
Abstract
It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and fibrations. (For endomorphisms of projective spaces, see version 1).
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds