Frontiers of Mathematics in China >

2007 , Vol. 2 >Issue 4: 623 - 637

DOI: https://doi.org/10.1007/s11464-007-0038-x

Decompositions of determinantal varieties

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  • School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;

Published date: 05 Dec 2007

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Abstract

In this paper, we study the irreducible decompositions of determinantal varieties of matrices given by rank conditions on upper left submatrices. Using the concept of essential rank function and the Ehresmann partial order on the set of all simple matrices, we design an algorithm to write a determinantal variety as a union of its irreducible components. This solves a problem raised by B. Sturmfels.

Cite this article

ZHAO Xu′an, GAO Hongzhu, SU Xiaole . Decompositions of determinantal varieties[J]. Frontiers of Mathematics in China, 2007 , 2(4) : 623 -637 . DOI: 10.1007/s11464-007-0038-x

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