PreprintarXiv licencearXiv
Automorphisms of hypersurfaces in polarized varieties
Abstract
Let F be a projective variety, let H be a normally generated line bundle on F, and let X∈ |H⊗ d| be a general projective variety. We establish a uniform criterion, formulated in terms of the graded Betti numbers of the section ring R(F,H), that provides sufficient conditions for every automorphism of X to extend to an automorphism of F. This extends the classical results of Matsumura-Monsky on automorphisms of hypersurfaces in projective spaces to a broader class of polarized varieties (F,H), including rational homogeneous varieties of Picard number one, smooth Fano threefolds with their anticanonical polarization, and examples of hyperkähler and Calabi-Yau varieties.
Related
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BibTeX
@misc{quedo2026automorphisms,
title = {{Automorphisms of hypersurfaces in polarized varieties}},
author = {Ana Quedo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00709},
eprint = {2610.00709},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00709},
}
RIS
TY - UNPB
TI - Automorphisms of hypersurfaces in polarized varieties
AU - Ana Quedo
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00709
UR - https://arxiv.org/abs/2610.00709
AB - Let F be a projective variety, let H be a normally generated line bundle on F, and let X∈ |H^⊗ d| be a general projective variety. We establish a uniform criterion, formulated in terms of the graded Betti numbers of the section ring R(F,H), that provides sufficient conditions for every automorphism of X to extend to an automorphism of F. This extends the classical results of Matsumura-Monsky on automorphisms of hypersurfaces in projective spaces to a broader class of polarized varieties (F,H), including rational homogeneous varieties of Picard number one, smooth Fano threefolds with their anticanonical polarization, and examples of hyperkähler and Calabi-Yau varieties.
ER -