Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces

Victoria Cantoral Fardan; Alice Garbagnati; Cecília Salgado Guimarães da Silva; Antonela Trbovic; Rosa Winter

doi:10.1007/978-3-030-77700-5_6

Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces

Victoria Cantoral Fardan
, Alice Garbagnati
, Cecília Salgado Guimarães da Silva
, Antonela Trbovic
, Rosa Winter

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

2 Citations (Scopus)

Abstract

We study K3 surfaces over a number field k which are double
covers of extremal rational elliptic surfaces. We provide a list of all elliptic
fibrations on certain K3 surfaces together with the degree of the field extension
over which each genus one fibration is defined and admits a section. We show
that the latter depends, in general, on the action of the cover involution on
the fibers of the genus 1 fibration.

Original language	English
Title of host publication	Women in Numbers Europe III
Subtitle of host publication	Research Directions in Number Theory
Editors	Alina Carmen Cojocaru, Sorina Ionica, Elisa Lorenzo García
Publisher	Springer
Pages	171-205
ISBN (Electronic)	978-3-030-77700-5
ISBN (Print)	978-3-030-77699-2
DOIs	https://doi.org/10.1007/978-3-030-77700-5_6
Publication status	Published - 2021
Externally published	Yes

Publication series

Name	Association for Women in Mathematics Series
Publisher	Springer
Volume	24

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10.1007/978-3-030-77700-5_6

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Cantoral Fardan, V., Garbagnati, A., Salgado Guimarães da Silva, C., Trbovic, A., & Winter, R. (2021). Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces. In A. C. Cojocaru, S. Ionica, & E. Lorenzo García (Eds.), Women in Numbers Europe III: Research Directions in Number Theory (pp. 171-205). (Association for Women in Mathematics Series; Vol. 24). Springer. https://doi.org/10.1007/978-3-030-77700-5_6

Cantoral Fardan, Victoria ; Garbagnati, Alice ; Salgado Guimarães da Silva, Cecília et al. / Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces. Women in Numbers Europe III: Research Directions in Number Theory. editor / Alina Carmen Cojocaru ; Sorina Ionica ; Elisa Lorenzo García. Springer, 2021. pp. 171-205 (Association for Women in Mathematics Series).

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title = "Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces",

abstract = "We study K3 surfaces over a number field k which are double covers of extremal rational elliptic surfaces. We provide a list of all elliptic fibrations on certain K3 surfaces together with the degree of the field extension over which each genus one fibration is defined and admits a section. We show that the latter depends, in general, on the action of the cover involution on the fibers of the genus 1 fibration.",

author = "\{Cantoral Fardan\}, Victoria and Alice Garbagnati and \{Salgado Guimar{\~a}es da Silva\}, Cec{\'i}lia and Antonela Trbovic and Rosa Winter",

year = "2021",

doi = "10.1007/978-3-030-77700-5\_6",

language = "English",

isbn = "978-3-030-77699-2",

series = "Association for Women in Mathematics Series",

publisher = "Springer",

pages = "171--205",

editor = "Cojocaru, \{Alina Carmen \} and Ionica, \{Sorina \} and \{Lorenzo Garc{\'i}a\}, \{Elisa \}",

booktitle = "Women in Numbers Europe III",

}

Cantoral Fardan, V, Garbagnati, A, Salgado Guimarães da Silva, C, Trbovic, A & Winter, R 2021, Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces. in AC Cojocaru, S Ionica & E Lorenzo García (eds), Women in Numbers Europe III: Research Directions in Number Theory. Association for Women in Mathematics Series, vol. 24, Springer, pp. 171-205. https://doi.org/10.1007/978-3-030-77700-5_6

Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces. / Cantoral Fardan, Victoria; Garbagnati, Alice; Salgado Guimarães da Silva, Cecília et al.
Women in Numbers Europe III: Research Directions in Number Theory. ed. / Alina Carmen Cojocaru; Sorina Ionica; Elisa Lorenzo García. Springer, 2021. p. 171-205 (Association for Women in Mathematics Series; Vol. 24).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces

AU - Cantoral Fardan, Victoria

AU - Garbagnati, Alice

AU - Salgado Guimarães da Silva, Cecília

AU - Trbovic, Antonela

AU - Winter, Rosa

PY - 2021

Y1 - 2021

N2 - We study K3 surfaces over a number field k which are double covers of extremal rational elliptic surfaces. We provide a list of all elliptic fibrations on certain K3 surfaces together with the degree of the field extension over which each genus one fibration is defined and admits a section. We show that the latter depends, in general, on the action of the cover involution on the fibers of the genus 1 fibration.

AB - We study K3 surfaces over a number field k which are double covers of extremal rational elliptic surfaces. We provide a list of all elliptic fibrations on certain K3 surfaces together with the degree of the field extension over which each genus one fibration is defined and admits a section. We show that the latter depends, in general, on the action of the cover involution on the fibers of the genus 1 fibration.

U2 - 10.1007/978-3-030-77700-5_6

DO - 10.1007/978-3-030-77700-5_6

M3 - Chapter

SN - 978-3-030-77699-2

T3 - Association for Women in Mathematics Series

SP - 171

EP - 205

BT - Women in Numbers Europe III

A2 - Cojocaru, Alina Carmen

A2 - Ionica, Sorina

A2 - Lorenzo García, Elisa

PB - Springer

ER -

Cantoral Fardan V, Garbagnati A, Salgado Guimarães da Silva C, Trbovic A, Winter R. Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces. In Cojocaru AC, Ionica S, Lorenzo García E, editors, Women in Numbers Europe III: Research Directions in Number Theory. Springer. 2021. p. 171-205. (Association for Women in Mathematics Series). doi: 10.1007/978-3-030-77700-5_6

Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces

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