ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 13C40, 13P10, 14M12, 16R10 Domokos, Mátyás, Mathematical Institute of the Hungarian Academy of Sciences Determinantal ideals of certain subspace arrangements Given a sequence μ_{1} < ⋯ < μ_{k} of non-negative integers with μ_{1} ≤ 1, we study the locus X of points (x_{1}, …, x_{n}) in ℂ^{n} (where n ≥ k) such that the n × k matrix (x_{i}^{μ_{j}}) has rank smaller than k. We present a Gröbner basis of the ideal of polynomials vanishing on X. Interesting special cases involve ideals of truncations of hyperplane arrangements related to complex pseudoreflection groups, and ideals appearing in the study of chromatic numbers of graphs. The result has consequences also in the theory of polynomial identities of matrices. Reference: Domokos, M., Polynomial ideals and identities of matrices, “Methods in Ring Theory”, Lecture Notes in Pure and Applied Mathematics 198, (1998), 83–95.