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On the matroid stratification of Grassmann varieties, specialization of coordinates, and a problem of N. White

✍ Scribed by Bernd Sturmfels


Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
506 KB
Volume
75
Category
Article
ISSN
0001-8708

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✦ 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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