Minkowski Decompositions for Generic Infinitesimal Newton-Okounkov Bodies of Arbitrary-Degree External Tensor Products on Products of Curves
Abstract
Explicit computations of generic infinitesimal Newton--Okounkov bodies are difficult even for varieties with simple product structure. We give an explicit formula in arbitrary dimension for positive-degree external tensor products on products of smooth projective curves. Writing d↓=(d1↓,…,dn↓) for the decreasing rearrangement of the degree vector and setting dn+1↓=0, the body admits the explicit Minkowski decomposition ∑j=1n(dj↓−dj+1↓)Sj(n), where the Sj(n) are the embedded simplices defined below. Using this description, we give a sharp criterion for equality in the Minkowski inclusion. A simultaneous relabeling argument also allows finitely many such bodies to be realized on a common very general locus of flags after independent decreasing rearrangements of their degree vectors.
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BibTeX
@misc{lu2026minkowski,
title = {{Minkowski Decompositions for Generic Infinitesimal Newton-Okounkov Bodies of Arbitrary-Degree External Tensor Products on Products of Curves}},
author = {Yi Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17469},
eprint = {2609.17469},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17469},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minkowski Decompositions for Generic Infinitesimal Newton-Okounkov Bodies of Arbitrary-Degree External Tensor Products on Products of Curves
AU - Yi Lu
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17469
UR - https://arxiv.org/abs/2609.17469
AB - Explicit computations of generic infinitesimal Newton--Okounkov bodies are difficult even for varieties with simple product structure. We give an explicit formula in arbitrary dimension for positive-degree external tensor products on products of smooth projective curves. Writing d^↓=(d_1^↓,…,d_n^↓) for the decreasing rearrangement of the degree vector and setting d_n+1^↓=0, the body admits the explicit Minkowski decomposition ∑_j=1^n(d_j^↓−d_j+1^↓)S_j^(n), where the S_j^(n) are the embedded simplices defined below. Using this description, we give a sharp criterion for equality in the Minkowski inclusion. A simultaneous relabeling argument also allows finitely many such bodies to be realized on a common very general locus of flags after independent decreasing rearrangements of their degree vectors.
ER -