Abstract
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We study relative deformation of a map into a Kähler manifold whose image is a
divisor. We show that if the map satisfies a condition called semiregularity, then it
allows relative deformations if and only if the cycle class of the image remains Hodge
in the family. This gives a refinement of the so-called variational Hodge conjecture.
We also show that the semiregularity of maps is related to classical notions such as
Cayley–Bacharach conditions and d-semistability.
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Keywords
deformation theory, Hodge theory, semiregularity
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Mathematical Subject Classification
Primary: 14C30, 32G10
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Milestones
Received: 4 October 2022
Revised: 10 December 2023
Accepted: 22 March 2024
Published: 30 April 2024
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