# When are multidegrees positive

@article{Castillo2020WhenAM,
title={When are multidegrees positive},
author={F. Castillo and Yairon Cid-Ruiz and Binglin Li and J. Monta{\~n}o and N. Zhang},
journal={arXiv: Algebraic Geometry},
year={2020}
}
Let $k$ be an arbitrary field, $P = P_k^{m_1} \times_k \cdots \times_k P_k^{m_p}$ be a multiprojective space over $k$, and $X \subseteq P$ be a closed subscheme of $P$. We provide necessary and sufficient conditions for the positivity of the multidegrees of $X$. As a consequence of our methods, we show that when $X$ is irreducible, the support of multidegrees forms a discrete algebraic polymatroid. In algebraic terms, we characterize the positivity of the mixed multiplicities of a standard… Expand
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