The main topic of this book is a study of invariants with respect to an action of a complex Lie group G on a compact complex manifold M. The action of G defines a decomposition ₣ of M to G-orbits. The decomposition ₣ is called L-foliation if ₣ coincides generically with a holomorphic foliation of M. Most attention is given to a study of L-foliations of codimension one in projective spaces. Basic properties of L-foliations are studied in chapter 1. Chapter 2 contains a lot of different examples of L-foliations of various actions on (complex) projective spaces. L-foliations of a low degree are studied in chapter 3. A particular case of L-foliations in dimension 3 is discussed in chapter 4. Quadratic L-foliations form a topic of chapter 5. The final chapter treats a particular case: L-foliations of degree 3 in dimension 4. The book contains some classification results in low dimensions.

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