• Corpus ID: 244714071

# Totally Invariant Divisors of non Trivial Endomorphisms of the Projective Space

@inproceedings{Yanis2021TotallyID,
title={Totally Invariant Divisors of non Trivial Endomorphisms of the Projective Space},
author={Mabed Yanis},
year={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 such a divisor. As a consequence, we prove the linearity of totally invariant divisors with isolated singularities.

## References

SHOWING 1-10 OF 12 REFERENCES
Totally invariant divisors of endomorphisms of projective spaces
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
Invariant hypersurfaces of endomorphisms of the projective 3-space
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
On Endomorphisms of Fano Manifolds of Picard Number One
• Mathematics
• 2011
Let X be a Fano manifold of Picard number one different from the projective space. It has been conjectured that a surjective endomorphism X → X must be bijective. In this article, we will prove a
Logarithmic sheaves attached to arrangements of hyperplanes
A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties,
Linearity of the exceptional set for maps of Pk(C)
• Mathematics
• 2004
Abstract.Let f be a holomorphic self-map of Pk(C), with degree larger than 2. We show that its exceptional set is a finite union of linear subspaces.
HIGHER DIMENSIONAL ALGEBRAIC GEOMETRY
• Mathematics
• 2006
I will talk about termination of flips in dimension 4 following AHacon-Kawamata and the work of Shokurov since then.
Singularities of varieties admitting an endomorphism
• Mathematics
• 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
Algebraic Geometry
Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)
Hypersurfaces exceptionnelles des endomorphismes de ℂℙ(n)
• Mathematics
• 2000
ResuméOn étudie les hypersurfaces exceptionnelles pour les applications holomorphes de ℂℙ(n). On montre qu'une telle hypersurface n'est jamais lisse dès que son degré est plus grand que
Complex dynamics in higher dimension
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