The graded Betti numbers are not tropical invariants
Noah Laikin
Abstract
We show that the graded Betti numbers are not invariants of the tropicalisation of a homogeneous ideal, or the tropicalisation of a projective algebraic scheme over a valued field. We do this by producing a family of saturated ideals that all realise the same tropical ideal with one member having a distinct Betti table from the rest.
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