Jumps, folds and hypercomplex structures

We investigate the geometry of the Kodaira moduli space M of sections of π : Z → P 1 , the normal bundle of which is allowed to jump from O ( 1 ) n to O ( 1 ) n - 2 m ⊕ O ( 2 ) m ⊕ O m . In particular, we identify the natural assumptions which guarantee that the Obata connection of the hypercomplex...

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Bibliographic Details
Published in:Manuscripta mathematica 2020-11, Vol.163 (3-4), p.291-298
Main Authors: Bielawski, Roger, Peternell, Carolin
Format: Article
Language:English
Subjects:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
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Summary:We investigate the geometry of the Kodaira moduli space M of sections of π : Z → P 1 , the normal bundle of which is allowed to jump from O ( 1 ) n to O ( 1 ) n - 2 m ⊕ O ( 2 ) m ⊕ O m . In particular, we identify the natural assumptions which guarantee that the Obata connection of the hypercomplex part of M extends to a logarithmic connection on M .
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-019-01160-7