Multigraded Apolarity

2016/01/23 by Gałązka, Maciej · 2 citations
#14M25 #14N15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.06211

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. 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)^* when X is ℙ¹ × ℙ¹, the Hirzebruch surface \mathbbF₁, the weighted projective plane ℙ(1,1,4), or a fake weighted projective plane.

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