Abstract:We establish three generalizations of the Küronya-Lozovanu jet separation criterion via Newton-Okounkov bodies: if an inverted standard simplex of size $n+k+\varepsilon$ is contained in all infinitesimal Newton-Okounkov bodies at $x$, then $K_X+D$ separates $k$-jets at $x$. We prove (1) a canonical-free version with a computable multiple $m(D)$; (2) a multipoint extension for simultaneous jet separation; and (3) a combination of both. Proofs use Trusiani's framework and Nadel vanishing. We conclude with explicit computations for a double cover of a product of elliptic curves.
| Subjects: | Algebraic Geometry (math.AG) |
| Cite as: | arXiv:2605.25185 [math.AG] |
| (or arXiv:2605.25185v1 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25185 arXiv-issued DOI via DataCite (pending registration) |
From: Yi Lu [view email]
[v1]
Sun, 24 May 2026 17:30:29 UTC (18 KB)
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