On volumes and the generic invariance of Fano type varieties

Fuente: arXiv
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Main Author: Kim, Donghyeon
Format: Preprint
Published: 2025
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_version_ 1866916961260142592
author Kim, Donghyeon
author_facet Kim, Donghyeon
contents We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset, or the Fano type fibers are dimension $2$. Additionally, paralleling this theorem, we establish a conjecture by Schwede and Smith under the condition that the volumes of anti-canonical divisors remain constant in the reduction mod $p$.
format Preprint
id arxiv_https___arxiv_org_abs_2506_13603
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On volumes and the generic invariance of Fano type varieties
Kim, Donghyeon
Algebraic Geometry
14E05, 14E30, 14J45, 14G17
We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset, or the Fano type fibers are dimension $2$. Additionally, paralleling this theorem, we establish a conjecture by Schwede and Smith under the condition that the volumes of anti-canonical divisors remain constant in the reduction mod $p$.
title On volumes and the generic invariance of Fano type varieties
topic Algebraic Geometry
14E05, 14E30, 14J45, 14G17
url https://arxiv.org/abs/2506.13603