Ballico, Edoardo The algebraic geometry and the deformation theory of the signed geodesics space. (English) Zbl 0929.53018 Ric. Mat. 47, No. 1, 1-12 (1998). 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 Keywords:deformation theory; quadric hypersurfaces; complex signed geodesic; normal bundle; rational curves; Moishezon variety PDFBibTeX XMLCite \textit{E. Ballico}, Ric. Mat. 47, No. 1, 1--12 (1998; Zbl 0929.53018)