Elliptic Fibrations on Covers of the Elliptic Modular Surface of Level 5

Francesca Balestrieri, Julie Desjardins, Alice Garbagnati, Celine Maistret, Cecília Salgado*, Isabel Vogt

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

6 Citations (Scopus)

Abstract

We consider the K3 surfaces that arise as double covers of the elliptic modular surface of level 5, R5,5. Such surfaces have a natural elliptic fibration induced by the fibration on R5,5. Moreover, they admit several other elliptic fibrations. We describe such fibrations in terms of linear systems of curves on R5,5. This has a major advantage over other methods of classification of elliptic fibrations, namely, a simple algorithm that has as input equations of linear systems of curves in the projective plane yields a Weierstrass equation for each elliptic fibration. We deal in detail with the cases for which the double cover is branched over the two reducible fibers of type I5 and for which it is branched over two smooth fibers, giving a complete list of elliptic fibrations for these two scenarios.
Original languageEnglish
Title of host publicationWomen in Numbers Europe II
Subtitle of host publicationContributions to Number Theory and Arithmetic Geometry
EditorsIrene I. Bouw, Ekin Ozman, Jennifer Johnson-Leung, Rachel Newton
PublisherSpringer
Pages159-197
Number of pages39
ISBN (Print)9783319749976, 9783319749983
DOIs
Publication statusPublished - 2018
Externally publishedYes

Publication series

NameAssociation for Women in Mathematics Series
PublisherSpringer
Volume11

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