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Hodge level and effective non-vanishing for smooth weighted complete intersections
Abstract
We prove that for every smooth well formed weighted complete intersection of general type of dimension n>0, the Hodge number h0,n(X) is positive; in other words, its Hodge level is maximal. We also obtain an explicit lower bound for the geometric genus pg(X). This implies that the only weighted complete intersection of general type that is not a numerical intersection with a linear cone with pg(X)=1 is X6,6⊂ℙ(1,2,2,3,3). We also prove the Ambro--Kawamata effective non-vanishing conjecture for smooth well formed weighted complete intersections.
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BibTeX
@misc{przyjalkowski2026hodge,
title = {{Hodge level and effective non-vanishing for smooth weighted complete intersections}},
author = {Victor Przyjalkowski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11825},
eprint = {2609.11825},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11825},
}
RIS
TY - UNPB
TI - Hodge level and effective non-vanishing for smooth weighted complete intersections
AU - Victor Przyjalkowski
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.11825
UR - https://arxiv.org/abs/2609.11825
AB - 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⊂ℙ(1,2,2,3,3). We also prove the Ambro--Kawamata effective non-vanishing conjecture for smooth well formed weighted complete intersections.
ER -