Decompositions of determinantal varieties

doi:10.1007/s11464-007-0038-x

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Front. Math. China ›› 2007, Vol. 2 ›› Issue (4) : 623-637. DOI: 10.1007/s11464-007-0038-x

Decompositions of determinantal varieties

ZHAO Xu′an, GAO Hongzhu, SU Xiaole

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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.

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ZHAO Xu′an, GAO Hongzhu, SU Xiaole. Decompositions of determinantal varieties. Front. Math. China, 2007, 2(4): 623‒637 https://doi.org/10.1007/s11464-007-0038-x