ON THE DETERMINANT OF A DUAL PERIODIC SINGULAR FIBER

Cheng Gong; Jun Lu; Sheng Li Tan

doi:10.4134/BKMS.b220710

ON THE DETERMINANT OF A DUAL PERIODIC SINGULAR FIBER

Cheng Gong, Jun Lu, Sheng Li Tan

School of Mathematical Sciences

Soochow University

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

Abstract

Let F be a periodic singular fiber of genus g with dual fiber F^∗, and let T (resp. T^∗) be the set of the components of F (resp. F^∗) by removing one component with multiplicity one. We give a formula to compute the determinant | det T | of the intersect form of T. As a consequence, we prove that | det T | = | det T^∗|. As an application, we compute the Mordell-Weil group of a fibration f: S → P¹ of genus 2 with two singular fibers.

Original language	English
Pages (from-to)	1365-1374
Number of pages	10
Journal	Bulletin of the Korean Mathematical Society
Volume	60
Issue number	5
DOIs	https://doi.org/10.4134/BKMS.b220710
State	Published - 1 Sep 2023

Keywords

Modell-Weil group
determinant
fibrations
singular fiber

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title = "ON THE DETERMINANT OF A DUAL PERIODIC SINGULAR FIBER",

abstract = "Let F be a periodic singular fiber of genus g with dual fiber F∗, and let T (resp. T∗) be the set of the components of F (resp. F∗) by removing one component with multiplicity one. We give a formula to compute the determinant | det T | of the intersect form of T. As a consequence, we prove that | det T | = | det T∗|. As an application, we compute the Mordell-Weil group of a fibration f: S → P1 of genus 2 with two singular fibers.",

keywords = "Modell-Weil group, determinant, fibrations, singular fiber",

author = "Cheng Gong and Jun Lu and Tan, \{Sheng Li\}",

note = "Publisher Copyright: {\textcopyright} 2023 Korean Mathematical Society.",

year = "2023",

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doi = "10.4134/BKMS.b220710",

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TY - JOUR

T1 - ON THE DETERMINANT OF A DUAL PERIODIC SINGULAR FIBER

AU - Gong, Cheng

AU - Lu, Jun

AU - Tan, Sheng Li

PY - 2023/9/1

Y1 - 2023/9/1

N2 - Let F be a periodic singular fiber of genus g with dual fiber F∗, and let T (resp. T∗) be the set of the components of F (resp. F∗) by removing one component with multiplicity one. We give a formula to compute the determinant | det T | of the intersect form of T. As a consequence, we prove that | det T | = | det T∗|. As an application, we compute the Mordell-Weil group of a fibration f: S → P1 of genus 2 with two singular fibers.

AB - Let F be a periodic singular fiber of genus g with dual fiber F∗, and let T (resp. T∗) be the set of the components of F (resp. F∗) by removing one component with multiplicity one. We give a formula to compute the determinant | det T | of the intersect form of T. As a consequence, we prove that | det T | = | det T∗|. As an application, we compute the Mordell-Weil group of a fibration f: S → P1 of genus 2 with two singular fibers.

KW - Modell-Weil group

KW - determinant

KW - fibrations

KW - singular fiber

UR - https://www.scopus.com/pages/publications/85174160316

U2 - 10.4134/BKMS.b220710

DO - 10.4134/BKMS.b220710

M3 - 文章

AN - SCOPUS:85174160316

SN - 1015-8634

VL - 60

SP - 1365

EP - 1374

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 5

ER -

ON THE DETERMINANT OF A DUAL PERIODIC SINGULAR FIBER

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Keywords

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