Calabi-Yau threefolds with boundary
File(s)
Published version
Author(s)
Donaldson, Simon
Lehmann, Fabian
Type
Journal Article
Abstract
In this paper we develop a deformation theory for complex Calabi-Yau threefolds with boundary, parallel to the theory for G2-structures developed in
[4]. Thus we consider a C∞ 6-manifold Z with boundary M = ∂Z and a
nowhere-zero holomorphic 3-form Ψ+iΨ, for real forms Ψ ˆ , Ψ. We address the ˆ
question: if Ψ|M is deformed to a nearby closed 3-form on M can we deform
the Calabi-Yau structure on Z to match? In our previous paper [5] we studied a variant of this question, for domains Z in a fixed ambient Calabi-Yau
threefold.
[4]. Thus we consider a C∞ 6-manifold Z with boundary M = ∂Z and a
nowhere-zero holomorphic 3-form Ψ+iΨ, for real forms Ψ ˆ , Ψ. We address the ˆ
question: if Ψ|M is deformed to a nearby closed 3-form on M can we deform
the Calabi-Yau structure on Z to match? In our previous paper [5] we studied a variant of this question, for domains Z in a fixed ambient Calabi-Yau
threefold.
Date Issued
2025-01-01
Date Acceptance
2024-09-11
Citation
Pure and Applied Mathematics Quarterly, 2025, 21 (3), pp.1119-1170
ISSN
1558-8599
Publisher
International Press
Start Page
1119
End Page
1170
Journal / Book Title
Pure and Applied Mathematics Quarterly
Volume
21
Issue
3
Copyright Statement
© 2024 International Press of Boston, Inc.
Subjects
Mathematics
Mathematics, Applied
Physical Sciences
Science & Technology
THEOREM
Publication Status
Published
Date Publish Online
2025-01-14