31. This consideration proves that the Picard group of a projective space is free of rank 1. 32. Since the right-hand side takes values in a projective space , is well-defined. 33. For another example, the complement of any conic in projective space of dimension 2 is affine. 34. In this way, every nondegenerate semilinear map induces a correlation of a projective space to itself. 35. Projective polytopes can be defined in higher dimension as tessellations of projective space in one less dimension. 36. Since fixes, the-orbit of in the complex projective space of coincides with the orbit and 37. That is, affine spaces are open subspaces of projective spaces , which are quotients of vector spaces. 38. Another generalization of projective spaces are weighted projective spaces; these are themselves special cases of toric varieties. 39. Another generalization of projective spaces are weighted projective spaces ; these are themselves special cases of toric varieties. 40. Homogeneous coordinates for projective spaces can also be created with elements from a division ring ( skewfield ).
