Deformations of fibered Calabi--Yau varieties

Fuente: arXiv
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Auteurs principaux: Bakker, Benjamin, DeVleming, Kristin, Filipazzi, Stefano, Laza, Radu, Li, Jennifer, Svaldi, Roberto, Wang, Chengxi, Zhao, Junyan
Format: Preprint
Publié: 2026
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author Bakker, Benjamin
DeVleming, Kristin
Filipazzi, Stefano
Laza, Radu
Li, Jennifer
Svaldi, Roberto
Wang, Chengxi
Zhao, Junyan
author_facet Bakker, Benjamin
DeVleming, Kristin
Filipazzi, Stefano
Laza, Radu
Li, Jennifer
Svaldi, Roberto
Wang, Chengxi
Zhao, Junyan
contents Kollár showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K$-torsion variety $X$ with $H^2(X,\mathcal{O}_X)=0$, using Hodge theoretic techniques and the $T^1$-lifting criterion of Kawamata--Ran. More generally, our strategy implies that even without the cohomological assumption, small deformations of a semiample line bundle on a smooth $K$-torsion variety remain semiample up to homological equivalence.
format Preprint
id arxiv_https___arxiv_org_abs_2604_14024
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Deformations of fibered Calabi--Yau varieties
Bakker, Benjamin
DeVleming, Kristin
Filipazzi, Stefano
Laza, Radu
Li, Jennifer
Svaldi, Roberto
Wang, Chengxi
Zhao, Junyan
Algebraic Geometry
High Energy Physics - Theory
Differential Geometry
Primary: 14D15, 14J32, Secondary: 14D07
Kollár showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K$-torsion variety $X$ with $H^2(X,\mathcal{O}_X)=0$, using Hodge theoretic techniques and the $T^1$-lifting criterion of Kawamata--Ran. More generally, our strategy implies that even without the cohomological assumption, small deformations of a semiample line bundle on a smooth $K$-torsion variety remain semiample up to homological equivalence.
title Deformations of fibered Calabi--Yau varieties
topic Algebraic Geometry
High Energy Physics - Theory
Differential Geometry
Primary: 14D15, 14J32, Secondary: 14D07
url https://arxiv.org/abs/2604.14024