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