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arXiv · 2608.06284

The graded Betti numbers are not tropical invariants

Noah Laikin
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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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Noah Laikin. 2026-08-06. The graded Betti numbers are not tropical invariants. https://arxiv.org/abs/2608.06284

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