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arXiv · 1906.06817

Gr\"obner bases and the Cohen-Macaulay property of Li's double determinantal varieties

Nathan Fieldsteel·Patricia Klein
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Abstract

We consider double determinantal varieties, a special case of Nakajima quiver varieties. Li conjectured that double determinantal varieties are normal, irreducible, Cohen-Macaulay varieties whose defining ideals have a Gr\"obner basis given by their natural generators. We use liaison theory to prove this conjecture in a manner that generalizes results for mixed ladder determinantal varieties. We also give a formula for the dimension of a double determinantal variety.

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Nathan Fieldsteel, Patricia Klein. 2019-06-17. Gr\"obner bases and the Cohen-Macaulay property of Li's double determinantal varieties. https://doi.org/10.1090/bproc%2F56

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