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The Linear Span of Four Points in the Plücker's Quadric in P5

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2014

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
Given four (distinct) lines l1, l2, l3, l4 in P3. Let Pi (i = 1,...,4) be the image of li in the Plücker's quadric â c P5 under the Plücker embedding & (in (1)). Set A = (P1,...,P4) be the linear span of those four points in P5. The purpose of this article is to write specifically what kind of quadric A nâ can be, taking under considerations all possible configurations of these four lines in P3. In particular, having in mind the classical problem in Schubert Calculus: How many lines in 3-space meet four given lines in general position? whose answer is 2 (see p. 272 in [3] or p. 746 in [4]). We verified that four lines in P3 are in general position if and only if A is a 3-plane and A nâ is an irreducible quadric surface. In fact, we prove that there are exactly two solutions if and only if A is a 3-plane and A n â is a nonsingular quadric.
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REFERENCES

References: 

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