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arXiv · 2009.01651

Deformation of pairs and semiregularity

Takeo Nishinou
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Abstract

In this paper, we study relative deformations of maps into a family of Kähler manifolds whose images are divisors. 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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Takeo Nishinou. 2020-09-03. Deformation of pairs and semiregularity. https://arxiv.org/abs/2009.01651

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