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ZARISKI PAIRS OF INDEX 19 AND MORDELL–WEIL GROUPS OF K3 SURFACES

Published online by Cambridge University Press:  01 January 2000

ENRIQUE ARTAL BARTOLO  and
HIRO-O TOKUNAGA
ENRIQUE ARTAL BARTOLO
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, Campus Plaza San Francisco s/n, E-50009 Zaragoza, [email protected]
HIRO-O TOKUNAGA
Affiliation:
Department of Mathematics, Kochi University, Kochi 780, [email protected]
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Abstract

We find Zariski pairs of sextics with simple singularities having maximal total Milnornumber. We also relate them to the existence of distinct Mordell--Weil groups of extremal elliptic $K3$ surfaces with a fixed set of semistable singular fibres.

1991 Mathematics Subject Classification: 14F45, 14F27, 14F28.

Keywords

sextic curves$K3$ surfaceselliptic fibrationAlexander polynomial
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 80 , Issue 1 , January 2000 , pp. 127 - 144
Copyright
2000 London Mathematical Society

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