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Abstract
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We give the classification of normal del Pezzo surfaces of rank one with at most log
canonical singularities containing the affine plane defined over an algebraically nonclosed
field of characteristic zero. As an application, we have a criterion for del Pezzo fibrations
with canonical singularities whose generic fibers are not smooth to contain vertical
-cylinders.
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Keywords
normal del Pezzo surface, compactification of the affine
plane, algebraically nonclosed field
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Mathematical Subject Classification
Primary: 14J26
Secondary: 14J17, 14J45, 14R10
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Milestones
Received: 16 May 2022
Revised: 25 October 2022
Accepted: 31 October 2022
Published: 21 March 2023
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| © 2022 MSP (Mathematical Sciences
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