The integral closedness of lattice simplices with large lattice length

Summary · qwen2.5:32b

The study proves that every $n$-dimensional lattice simplex $P$, where the lattice length $L(P)\ge n-1$, is integrally closed, impacting the understanding of projective normality for ample line bundles on $\mathbb{Q}$-factorial toric Fano varieties with Picard number one. A key detail involves refining this result using the invariant $\Gamma_{P}$.

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Exploring the proof of integrally closed lattice simplices and its implications for projective normality in toric Fano varieties with Picard number one.

Excerpt

arXiv:2606.16348v2 Announce Type: replace Abstract: We prove that every $n$-dimensional lattice simplex $P$ whose lattice length $L(P)\ge n-1$ is integrally closed. As an application, we obtain a simple criterion for the projective normality of ample line bundles on $\mathbb{Q}$-factorial toric Fano varieties with Picard number one. We further obtain a refinement of this result in terms of the invariant $\Gamma_{P}$.