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Singularities of totally invariant hypersurfaces of endomorphisms

  • Amaël Broustet
  • Andreas Höring
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Abstract

Let f: X→ X be a polarised endomorphism of a complex projective manifold, and let D⊂ X be a reduced totally invariant hypersurface. We prove that every irreducible component of the singular locus of D has codimension one in D. In particular, if D is normal, then it is smooth. As an application we prove the linearity of totally invariant divisors for endomorphisms of ℙ4.

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Cite

BibTeXRIS
BibTeX
@misc{broustet2026singularities,
  title = {{Singularities of totally invariant hypersurfaces of endomorphisms}},
  author = {Amaël Broustet and Andreas Höring},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08633},
  eprint = {2609.08633},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05745951v1},
}
RIS
TY  - UNPB
TI  - Singularities of totally invariant hypersurfaces of endomorphisms
AU  - Amaël Broustet
AU  - Andreas Höring
PY  - 2026
DA  - 2026/09/08
PB  - HAL
DO  - 10.48550/arxiv.2609.08633
UR  - https://hal.science/hal-05745951v1
AB  - Let f: X→ X be a polarised endomorphism of a complex projective manifold, and let D⊂ X be a reduced totally invariant hypersurface. We prove that every irreducible component of the singular locus of D has codimension one in D. In particular, if D is normal, then it is smooth. As an application we prove the linearity of totally invariant divisors for endomorphisms of ℙ^4.
ER  -