Singular fibers and Kodaira dimensions

Xin Lu; Sheng Li Tan; Kang Zuo

doi:10.1007/s00208-017-1528-0

Singular fibers and Kodaira dimensions

Xin Lu
, Sheng Li Tan^*
, Kang Zuo

^*Corresponding author for this work

School of Mathematical Sciences

Johannes Gutenberg University Mainz

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

5 Scopus citations

Abstract

Let f:X→P1 be a non-isotrivial semi-stable family of varieties of dimension m over P¹ with s singular fibers. Assume that the smooth fibers F are minimal, i.e., their canonical line bundles are semiample. Then κ(X) ≤ κ(F) + 1. If κ(X) = κ(F) + 1 , then sCloseSPigtSPi4m+2. If κ(X) ≥ 0 , then s≥4m+2. In particular, if m= 1 , s= 6 and κ(X) = 0 , then the family f is Teichmüller.

Original language	English
Pages (from-to)	1717-1728
Number of pages	12
Journal	Mathematische Annalen
Volume	370
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-017-1528-0
State	Published - 1 Apr 2018

Keywords

14D06
14H10
14J29

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10.1007/s00208-017-1528-0

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@article{1c6079857fc3498f88a24f8dc18bdac7,

title = "Singular fibers and Kodaira dimensions",

abstract = "Let f:X→P1 be a non-isotrivial semi-stable family of varieties of dimension m over P1 with s singular fibers. Assume that the smooth fibers F are minimal, i.e., their canonical line bundles are semiample. Then κ(X) ≤ κ(F) + 1. If κ(X) = κ(F) + 1 , then sCloseSPigtSPi4m+2. If κ(X) ≥ 0 , then s≥4m+2. In particular, if m= 1 , s= 6 and κ(X) = 0 , then the family f is Teichm{\"u}ller.",

keywords = "14D06, 14H10, 14J29",

author = "Xin Lu and Tan, \{Sheng Li\} and Kang Zuo",

note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag Berlin Heidelberg.",

year = "2018",

month = apr,

day = "1",

doi = "10.1007/s00208-017-1528-0",

language = "英语",

volume = "370",

pages = "1717--1728",

journal = "Mathematische Annalen",

issn = "0025-5831",

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}

TY - JOUR

T1 - Singular fibers and Kodaira dimensions

AU - Lu, Xin

AU - Tan, Sheng Li

AU - Zuo, Kang

PY - 2018/4/1

Y1 - 2018/4/1

N2 - Let f:X→P1 be a non-isotrivial semi-stable family of varieties of dimension m over P1 with s singular fibers. Assume that the smooth fibers F are minimal, i.e., their canonical line bundles are semiample. Then κ(X) ≤ κ(F) + 1. If κ(X) = κ(F) + 1 , then sCloseSPigtSPi4m+2. If κ(X) ≥ 0 , then s≥4m+2. In particular, if m= 1 , s= 6 and κ(X) = 0 , then the family f is Teichmüller.

AB - Let f:X→P1 be a non-isotrivial semi-stable family of varieties of dimension m over P1 with s singular fibers. Assume that the smooth fibers F are minimal, i.e., their canonical line bundles are semiample. Then κ(X) ≤ κ(F) + 1. If κ(X) = κ(F) + 1 , then sCloseSPigtSPi4m+2. If κ(X) ≥ 0 , then s≥4m+2. In particular, if m= 1 , s= 6 and κ(X) = 0 , then the family f is Teichmüller.

KW - 14D06

KW - 14H10

KW - 14J29

UR - https://www.scopus.com/pages/publications/85014576005

U2 - 10.1007/s00208-017-1528-0

DO - 10.1007/s00208-017-1528-0

M3 - 文章

AN - SCOPUS:85014576005

SN - 0025-5831

VL - 370

SP - 1717

EP - 1728

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

Singular fibers and Kodaira dimensions

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Keywords

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