Deformations of calibrations, {Calabi-Yau, HyperK\"ahler, $G_2$ and Spin(7) structures}

Ryushi Goto

Deformations of calibrations, {Calabi-Yau, HyperK\"ahler, $G_2$ and Spin(7) structures}

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arxiv math/0204288 v2 pith:ANCSSO4U submitted 2002-04-24 math.DG

Ryushi Goto This is my paper · ORCID

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keywords structurestheoryahlercalabi-yaudeformationdeformationsgeometrichyperk

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abstract

We shall develop a new deformation theory of geometric structures in terms of closed differential forms. This theory is a generalization of Kodaira -Spencer theory and further we obtain a criterion of unobstructed deformations. We apply this theory to certain geometric structures: Calabi-Yau, HyperK\"ahler, $\G$ and $\Spin$ structures and show that these deformation spaces are smooth in a systematic way.

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Spin(7)-Orbifold Resolutions
math.DG 2025-09 conditional novelty 7.0 of 10

New gluing framework produces torsion-free Spin(7)-manifolds resolving compact Spin(7)-orbifolds, with the gluing obstruction shown equivalent to matching Chen-Ruan cohomology in the codimension-four case.

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