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arXiv · 2609.11825

Maximality of the Hodge level for smooth weighted complete intersections of general type

Victor Przyjalkowski
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Abstract

We prove that for every smooth well formed weighted complete intersection of general type of dimension $n>0$, the Hodge number $h^{0,n}(X)$ is positive; in other words, its Hodge level is maximal. We also obtain an explicit lower bound for the geometric genus $p_g(X)$. This implies that the only weighted complete intersection of general type that is not a numerical intersection with a linear cone with $p_g(X)=1$ is $X_{6,6}\subset\mathbb{P}(1,2,2,3,3)$.

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Victor Przyjalkowski. 2026-09-10. Maximality of the Hodge level for smooth weighted complete intersections of general type. https://arxiv.org/abs/2609.11825

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