# Invariant hypersurfaces of endomorphisms of the projective 3-space

@article{Zhang2011InvariantHO, title={Invariant hypersurfaces of endomorphisms of the projective 3-space}, author={De-Qi Zhang}, journal={arXiv: Algebraic Geometry}, year={2011} }

We consider surjective endomorphisms f of degree > 1 on the projective n-space with n = 3, and f^{-1}-stable hypersurfaces V. We show that V is a hyperplane (i.e., deg(V) = 1) but with four possible exceptions; it is conjectured that deg(V) = 1 for any n > 1.

## 5 Citations

Totally Invariant Divisors of non Trivial Endomorphisms of the Projective Space

- Mathematics
- 2021

It is expected that a totally invariant divisor of a non-isomorphic endomorphism of the complex projective space is a union of hyperplanes. In this paper, we compute an upper bound for the degree of…

Totally invariant divisors of endomorphisms of projective spaces

- Mathematics
- 2016

Totally invariant divisors of endomorphisms of the projective space are expected to be always unions of linear spaces. Using logarithmic differentials we establish a lower bound for the degree of the…

Singularities of varieties admitting an endomorphism

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- 2012

Let $$X$$X be a normal variety such that $$K_X$$KX is $$\mathbb {Q}$$Q-Cartier, and let $$f:X \rightarrow X$$f:X→X be a finite surjective morphism of degree at least two. We establish a close…

Equidistribution of Preimages in Nonarchimedean Dynamics

- Mathematics
- 2013

Nonarchimedean dynamics is a young branch of dynamics that runs parallel to (and has interactions with) the more classical field of complex dynamics. In this talk, I will discuss some of the…

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