Multigraded apolarity

Maciej Gałązka

Mathematische Nachrichten, 2023, vol. 296, issue 1, 286-313

Abstract: We generalize methods to compute various kinds of rank to the case of a toric variety X embedded into projective space using a very ample line bundle L$\mathcal {L}$. We find an upper bound on the cactus rank. We use this to compute rank, border rank, and cactus rank of monomials in H0(X,L)∗$H^0(X, \mathcal {L})^*$ when X is P1×P1$\mathbb {P}^1 \times \mathbb {P}^1$, the Hirzebruch surface F1$\mathbb {F}_1$, or the weighted projective plane P(1,1,4)$\mathbb {P}(1,1,4)$.

Date: 2023
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https://doi.org/10.1002/mana.202000484

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