PreprintCC BY-NC-ND 4.0arXiv
Orbit Transversality for Projective Space
Abstract
Let f: ℙn→ ℙn be a dominant endomorphism defined over a number field K. We show that there is a finite extension L/K such that every proper closed subset of ℙn misses at least one grand (f,L)-orbit. Equivalently, (ℙn,f,K) is strongly dense orbit transversal (S-DOT): every set containing exactly one representative of each grand (f,L)-orbit is Zariski dense in ℙn.
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BibTeX
@misc{lu2026orbit,
title = {{Orbit Transversality for Projective Space}},
author = {Kaiwen Lu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05679},
eprint = {2611.05679},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05679},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Orbit Transversality for Projective Space
AU - Kaiwen Lu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05679
UR - https://arxiv.org/abs/2611.05679
AB - Let f: ℙ^n→ ℙ^n be a dominant endomorphism defined over a number field K. We show that there is a finite extension L/K such that every proper closed subset of ℙ^n misses at least one grand (f,L)-orbit. Equivalently, (ℙ^n,f,K) is strongly dense orbit transversal (S-DOT): every set containing exactly one representative of each grand (f,L)-orbit is Zariski dense in ℙ^n.
ER -