TY - CHAP
T1 - Elliptic Fibrations on Covers of the Elliptic Modular Surface of Level 5
AU - Balestrieri, Francesca
AU - Desjardins, Julie
AU - Garbagnati, Alice
AU - Maistret, Celine
AU - Salgado, Cecília
AU - Vogt, Isabel
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
U2 - 10.1007/978-3-319-74998-3_9
DO - 10.1007/978-3-319-74998-3_9
M3 - Chapter
SN - 9783319749976
SN - 9783319749983
T3 - Association for Women in Mathematics Series
SP - 159
EP - 197
BT - Women in Numbers Europe II
A2 - Bouw, Irene I.
A2 - Ozman, Ekin
A2 - Johnson-Leung, Jennifer
A2 - Newton, Rachel
PB - Springer
ER -