We show that every nondegenerate polar space of rank at least 4 with at least three points on each line can be embedded in a projective space. Together with some results from [9] and [12], this provides a particularly elementary proof that any such polar space is of classical type. Our methods involve the use of geometric hyperplanes and work equally well for spaces of finite or infinite rank.
Cuypers, H., Johnson, P., Pasini, A. (1992). On the embeddability of polar spaces. GEOMETRIAE DEDICATA, 44(3), 349-358 [10.1007/BF00181400].
On the embeddability of polar spaces
PASINI, ANTONIO
1992-01-01
Abstract
We show that every nondegenerate polar space of rank at least 4 with at least three points on each line can be embedded in a projective space. Together with some results from [9] and [12], this provides a particularly elementary proof that any such polar space is of classical type. Our methods involve the use of geometric hyperplanes and work equally well for spaces of finite or infinite rank.
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https://hdl.handle.net/11365/7093
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