The order of non-ordinary points under a blow-up
Research reports of National institute of technology, Ube College Volume 72
Page 57-63
published_at 2026-03
Title
The order of non-ordinary points under a blow-up
Creators
Shirato Tomoaki
Source Identifiers
[PISSN] 0386-4359
[NCID] AN00019833
Creator Keywords
genus one fibration
non-ordinary point
Frobenius morphism
1. Introduction
Abstract : Let π: X → C be a relatively minimal genus one fibration and assume that R 1 π∗
OX
is locally free. Let b : eX
→ X be a blow-up at a smooth point x ∈π− 1 (y) . We will show that
the order of non-ordinary point y ∈C is equal to the length of the higher direct image of the
cokernel of the relative Frobenius morphism of π◦ b at y.
OX
is locally free. Let b : eX
→ X be a blow-up at a smooth point x ∈π− 1 (y) . We will show that
the order of non-ordinary point y ∈C is equal to the length of the higher direct image of the
cokernel of the relative Frobenius morphism of π◦ b at y.
Resource Type
departmental bulletin paper
Publishers
宇部工業高等専門学校
Date Issued
2026-03
File Version
Version of Record
Access Rights
open access