Embeddings of real projective spaces
نویسندگان
چکیده
منابع مشابه
Embeddings of Real Projective Spaces
The question of finding the smallest Euclidean space in which real projective space P n can be (differentiably) embedded was the subject of intense investigation during the 1960s and 1970s. The purpose of this paper is to survey the status of the question, and add a little bit to our knowledge by proving one new family of embeddings, using old methods of obstruction theory. Our new result is gi...
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Theorem 1.1(1) improves on the previously best known result ([1]) by 1 dimension, while Theorem 1.1(2) improves on the previously best known nonimmersion and nonembedding results ([2]) for P 16n+10 and P 16n+11 by 4 dimensions, and is within 1 of best possible for them. It also implies new nonimmersions for P , P , and P . Theorem 1.2 improves on the previously best known embedding ([11]) of P ...
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We classify all embeddings θ : PG(n, q) −→ PG(d, q), with d ≥ n(n+3) 2 , such that θ maps the set of points of each line to a set of coplanar points and such that the image of θ generates PG(d, q). It turns out that d = 1 2n(n+3) and all examples are related to the quadric Veronesean of PG(n, q) in PG(d, q) and its projections from subspaces of PG(d, q) generated by sub-Veroneseans (the point s...
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We classify all embeddings θ : PG(n,K) −→ PG(d,F), with d ≥ n(n+3) 2 and K,F skew fields with |K| > 2, such that θ maps the set of points of each line of PG(n,K) to a set of coplanar points of PG(d,F), and such that the image of θ generates PG(d,F). It turns out that d = 12n(n+ 3) and all examples “essentially” arise from a similar “full” embedding θ′ : PG(n,K) −→ PG(d,K) by identifying K with ...
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We prove that fourth Veronese embeddings of projective spaces satisfies property N9. This settle the Ottaviani-Paoletti conjecture for fourth Veronese embeddings.
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ژورنال
عنوان ژورنال: Topology
سال: 1971
ISSN: 0040-9383
DOI: 10.1016/0040-9383(71)90024-3