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Abstract
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We show, in this third part, that the maximal number of singular points of a normal quartic surface
defined over an
algebraically closed field
of characteristic
is at
most
, if the minimal
resolution of
is not
a supersingular
surface. We also provide a family of explicit examples, valid in any characteristic.
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Keywords
normal quartic surface, $\mathrm{K3}$ surface, elliptic
fibration, rational double point
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Mathematical Subject Classification
Primary: 14J17, 14J25, 14J28, 14N05, 14N25
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Milestones
Received: 12 October 2022
Revised: 12 February 2023
Accepted: 26 February 2023
Published: 2 November 2023
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