On the matroid stratification of Grassmann varieties, specialization of coordinates, and a problem of N. White
β Scribed by Bernd Sturmfels
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 506 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
β¦ Synopsis
We resolve a problem of N. White [J. Combin. Theory Ser. B 29 (1980), 168-1751 by constructing representable matroids F and G with F< G in the weak map order such that no coordinatization of G specializes to a coordinatization of F. Our approach is based upon the interplay of combinatorics and topology in the matroid stratilication of the complex Grassmann variety G,,d introduced by 1. M. Gelfand, R. M. Goresky, R. D. MacPherson, and V. Serganova [Ado. in Math. 63 (1987) 301-3161. Related aspects and open problems in the algebraic geometry of matroids are discussed.
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