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arXiv · 2610.00709

Automorphisms of hypersurfaces in polarized varieties

Ana Quedo
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Abstract

Let $F$ be a projective variety, let $H$ be a normally generated line bundle on $F$, and let $X\in |H^{\otimes d}|$ 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.

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Ana Quedo. 2026-09-30. Automorphisms of hypersurfaces in polarized varieties. https://arxiv.org/abs/2610.00709

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