Structure of geometrically non-reduced varieties

Lena Ji; Joe Waldron

doi:10.1090/tran/8388

Structure of geometrically non-reduced varieties

Lena Ji
, Joe Waldron

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a structural result for geometrically non-reduced varieties and give applications to Fano varieties. For example, we show that if X is the generic fibre of a Mori fibre space of relative dimension n, and the characteristic is p > 2n + 1, then any geometric non-reducedness of X comes from the base of some fibration.

Original language	English (US)
Pages (from-to)	8333-8363
Number of pages	31
Journal	Transactions of the American Mathematical Society
Volume	374
Issue number	12
DOIs	https://doi.org/10.1090/tran/8388
State	Published - 2021
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/tran/8388

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abstract = "We prove a structural result for geometrically non-reduced varieties and give applications to Fano varieties. For example, we show that if X is the generic fibre of a Mori fibre space of relative dimension n, and the characteristic is p > 2n + 1, then any geometric non-reducedness of X comes from the base of some fibration.",

author = "Lena Ji and Joe Waldron",

note = "This material is based upon work of the first author while supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1656466; and of the second author while supported by the National Science Foundation under Grant No. 1440140, while he was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring of 2019. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.",

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PY - 2021

Y1 - 2021

N2 - We prove a structural result for geometrically non-reduced varieties and give applications to Fano varieties. For example, we show that if X is the generic fibre of a Mori fibre space of relative dimension n, and the characteristic is p > 2n + 1, then any geometric non-reducedness of X comes from the base of some fibration.

AB - We prove a structural result for geometrically non-reduced varieties and give applications to Fano varieties. For example, we show that if X is the generic fibre of a Mori fibre space of relative dimension n, and the characteristic is p > 2n + 1, then any geometric non-reducedness of X comes from the base of some fibration.

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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Structure of geometrically non-reduced varieties

Abstract

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