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Regularization and algebraic stability of birational automorphisms
Abstract
We compare five natural classes of birational automorphisms of an algebraic variety: projectively regularizable, regularizable, projectively pseudo-regularizable, pseudo-regularizable, and those admitting an algebraically stable model. These classes provide different geometric frameworks in which the dynamics of a birational automorphism, and in particular its first dynamical degree, can be studied. We determine the general inclusion relations among them and show that, for ℙk with kgeqslant 3, all the resulting non-trivial inclusions are strict; we prove this by giving explicit examples.
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BibTeX
@misc{kuznetsova2026regularization,
title = {{Regularization and algebraic stability of birational automorphisms}},
author = {Alexandra Kuznetsova},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02536},
eprint = {2610.02536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02536},
}
RIS
TY - UNPB
TI - Regularization and algebraic stability of birational automorphisms
AU - Alexandra Kuznetsova
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02536
UR - https://arxiv.org/abs/2610.02536
AB - We compare five natural classes of birational automorphisms of an algebraic variety: projectively regularizable, regularizable, projectively pseudo-regularizable, pseudo-regularizable, and those admitting an algebraically stable model. These classes provide different geometric frameworks in which the dynamics of a birational automorphism, and in particular its first dynamical degree, can be studied. We determine the general inclusion relations among them and show that, for ℙ^k with kgeqslant 3, all the resulting non-trivial inclusions are strict; we prove this by giving explicit examples.
ER -