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Multigraded apolarity

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  • Maciej Gałązka

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)$\mathbb {P}(1,1,4)$.

Suggested Citation

  • Maciej Gałązka, 2023. "Multigraded apolarity," Mathematische Nachrichten, Wiley Blackwell, vol. 296(1), pages 286-313, January.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:1:p:286-313
    DOI: 10.1002/mana.202000484
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