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The algebraic geometry and the deformation theory of the signed geodesics space. (English) Zbl 0929.53018

Summary: We discuss the algebraic geometric properties of the complex space parametrizing signed geodesics of a holomorphic Riemannian manifold. A key is deformation theory. Most of the proofs are cohomological computations. We also discuss what type of properties are preserved if we allow suitable limit objects in a partial compactification of this parameter space.

MSC:

53C22 Geodesics in global differential geometry
32G10 Deformations of submanifolds and subspaces
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14N05 Projective techniques in algebraic geometry
32G08 Deformations of fiber bundles
32J99 Compact analytic spaces
53C56 Other complex differential geometry
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