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Mathematics of Computation

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Rational double points on supersingular $K3$ surfaces

Author: Ichiro Shimada
Journal: Math. Comp. 73 (2004), 1989-2017
MSC (2000): Primary 14J28; Secondary 14J17, 14J27, 14Q10
Published electronically: March 18, 2004
MathSciNet review: 2059747
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Abstract: We investigate configurations of rational double points with the total Milnor number $21$ on supersingular $K3$ surfaces. The complete list of possible configurations is given. As an application, we also give the complete list of extremal (quasi-)elliptic fibrations on supersingular $K3$ surfaces.

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Additional Information

Ichiro Shimada
Affiliation: Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan

Keywords: Rational double point, supersingular $K3$ surface, extremal \mbox{(quasi-)} elliptic fibration
Received by editor(s): November 27, 2002
Published electronically: March 18, 2004
Article copyright: © Copyright 2004 American Mathematical Society