Gröbner bases and the Cohen-Macaulay property of Li’s double determinantal varieties

Fieldsteel, Nathan; Klein, Patricia

doi:10.1090/bproc/56

Gröbner bases and the Cohen-Macaulay property of Li’s double determinantal varieties
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by Nathan Fieldsteel and Patricia Klein HTML | PDF

Proc. Amer. Math. Soc. Ser. B 7 (2020), 142-158

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 Gröbner 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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