# The syzygies of some thickenings of determinantal varieties

@article{Raicu2014TheSO, title={The syzygies of some thickenings of determinantal varieties}, author={Claudiu Raicu and Jerzy Weyman}, journal={arXiv: Commutative Algebra}, year={2014} }

The vector space of m x n complex matrices (m >= n) admits a natural action of the group GL = GL_m x GL_n via row and column operations. For positive integers a,b, we consider the ideal I_{a x b} defined as the smallest GL-equivariant ideal containing the b-th powers of the a x a minors of the generic m x n matrix. We compute the syzygies of the ideals I_{a x b} for all a,b, together with their GL-equivariant structure, generalizing earlier results of Lascoux for the ideals of minors (b=1), and…

## 13 Citations

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