A boundary divisor in the moduli spaces of stable quintic surfaces
2017 ◽
Vol 28
(04)
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pp. 1750021
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We give a bound on which singularities may appear on Kollár–Shepherd-Barron–Alexeev stable surfaces for a wide range of topological invariants and use this result to describe all stable numerical quintic surfaces (KSBA-stable surfaces with [Formula: see text]) whose unique non-Du Val singularity is a Wahl singularity. We then extend the deformation theory of Horikawa to the log setting in order to describe the boundary divisor of the moduli space [Formula: see text] corresponding to these surfaces. Quintic surfaces are the simplest examples of surfaces of general type and the question of describing their moduli is a long-standing question in algebraic geometry.
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2012 ◽
Vol 148
(4)
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pp. 1051-1084
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2014 ◽
Vol 16
(02)
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pp. 1350010
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1992 ◽
pp. 166-175
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2012 ◽
Vol 106
(2)
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pp. 225-286
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2015 ◽
Vol 64
(3)
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pp. 483-492
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2013 ◽
Vol 65
(1)
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pp. 195-221
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