Deformation of pairs and semiregularity
Algebraic Geometry
2020-09-04 v1
Abstract
In this paper, we study relative deformations of maps into a family of K\"ahler 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.
Cite
@article{arxiv.2009.01651,
title = {Deformation of pairs and semiregularity},
author = {Takeo Nishinou},
journal= {arXiv preprint arXiv:2009.01651},
year = {2020}
}