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<p>We compute the generic infinitesimal Newton–Okounkov body of a natural polarization on products of curves. This appears to be the first nontrivial full description of such a body in arbitrary dimension. We also provide the first known examples of non-simplicial bodies in dimension 3.</p>

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Infinitesimal Newton–Okounkov bodies on products of curves

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Mihai Fulger,
  • Victor Lozovanu

摘要

We compute the generic infinitesimal Newton–Okounkov body of a natural polarization on products of curves. This appears to be the first nontrivial full description of such a body in arbitrary dimension. We also provide the first known examples of non-simplicial bodies in dimension 3.