On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1

Xin Lu; Sheng Li Tan; Wan Yuan Xu; Kang Zuo

doi:10.1016/j.matpur.2015.11.011

On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1

Xin Lu, Sheng Li Tan, Wan Yuan Xu, Kang Zuo

School of Mathematical Sciences

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

5 Scopus citations

Abstract

Let f:X→P1 be a non-isotrivial family of semi-stable curves of genus g≥1 defined over an algebraically closed field k. Denote by s_nc the number of the singular fibers whose Jacobians are non-compact. We prove that s_nc≥5 if k=C and g≥5; we also prove that s_nc≥4 if char(k)>0 and the relative Jacobian of f is non-smooth.

Original language	English
Pages (from-to)	724-733
Number of pages	10
Journal	Journal des Mathematiques Pures et Appliquees
Volume	105
Issue number	5
DOIs	https://doi.org/10.1016/j.matpur.2015.11.011
State	Published - 1 May 2016

Keywords

Family of curves
Non-compact Jacobian
Singular fiber

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10.1016/j.matpur.2015.11.011

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title = "On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1",

abstract = "Let f:X→P1 be a non-isotrivial family of semi-stable curves of genus g≥1 defined over an algebraically closed field k. Denote by snc the number of the singular fibers whose Jacobians are non-compact. We prove that snc≥5 if k=C and g≥5; we also prove that snc≥4 if char(k)>0 and the relative Jacobian of f is non-smooth.",

keywords = "Family of curves, Non-compact Jacobian, Singular fiber",

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

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T1 - On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1

AU - Lu, Xin

AU - Tan, Sheng Li

AU - Xu, Wan Yuan

AU - Zuo, Kang

PY - 2016/5/1

Y1 - 2016/5/1

N2 - Let f:X→P1 be a non-isotrivial family of semi-stable curves of genus g≥1 defined over an algebraically closed field k. Denote by snc the number of the singular fibers whose Jacobians are non-compact. We prove that snc≥5 if k=C and g≥5; we also prove that snc≥4 if char(k)>0 and the relative Jacobian of f is non-smooth.

AB - Let f:X→P1 be a non-isotrivial family of semi-stable curves of genus g≥1 defined over an algebraically closed field k. Denote by snc the number of the singular fibers whose Jacobians are non-compact. We prove that snc≥5 if k=C and g≥5; we also prove that snc≥4 if char(k)>0 and the relative Jacobian of f is non-smooth.

KW - Family of curves

KW - Non-compact Jacobian

KW - Singular fiber

UR - https://www.scopus.com/pages/publications/84958554886

U2 - 10.1016/j.matpur.2015.11.011

DO - 10.1016/j.matpur.2015.11.011

M3 - 文章

AN - SCOPUS:84958554886

SN - 0021-7824

VL - 105

SP - 724

EP - 733

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 5

ER -

On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1

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