Box-shaped matrices and the defining ideal of certain blowup surfaces
✍ Scribed by Huy Tài Hà
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 192 KB
- Volume
- 167
- Category
- Article
- ISSN
- 0022-4049
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✦ Synopsis
In this paper, we generalize the notions of a matrix and its ideal of 2 × 2 minors to that of a box-shaped matrix and its ideal of 2 × 2 minors, and make use of these notions to study projective embeddings of certain blowup surfaces. We prove that the ideal of 2 × 2 minors of a generic box-shaped matrix is a perfect prime ideal that gives the algebraic description for the Segre embedding of the product of several projective spaces. We use the notion of the ideal of 2 × 2 minors of a box-shaped matrix to give an explicit description for the deÿning ideal of the blowup of P 2 along a set of ( d+12 ) (d ∈ Z) points in generic position, embedded into projective spaces using very ample divisors which correspond to the linear systems of plane curves going through these points.